Updated on 2024/06/14

写真a

 
SUZUKI Yusuke
 
Organization
Academic Assembly Institute of Science and Technology Fundamental Sciences Professor
Graduate School of Science and Technology Fundamental Sciences Professor
Faculty of Science Department of Science Professor
Title
Professor
External link

Degree

  • 博士(学術) ( 2004.3   横浜国立大学 )

Research Interests

  • quadrangulation

  • triangulation

  • 1-Planar graph

  • local transformation

  • re-embedding structure

  • graph theory

  • topological graph theory

Research Areas

  • Natural Science / Basic mathematics

  • Natural Science / Applied mathematics and statistics

Research History (researchmap)

  • Niigata University   Faculty of Science Department of Science   Professor

    2024.4

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  • Niigata University   Faculty of Science Department of Science   Associate Professor

    2017.4 - 2023.3

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  • Niigata University   Faculty of Science Department of Mathematics Mathematical Analysis   Associate Professor

    2011.4 - 2017.3

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  • Tsuruoka National College of Technology   Associate Professor

    2008.1 - 2011.3

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  • Tsuruoka National College of Technology   Lecturer

    2004.4 - 2008.12

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Research History

  • Niigata University   Department of Science, Faculty of Science   Professor

    2024.4

  • Niigata University   Fundamental Sciences, Graduate School of Science and Technology   Professor

    2024.4

  • Niigata University   Fundamental Sciences, Institute of Science and Technology, Academic Assembly   Professor

    2024.4

  • Niigata University   Faculty of Science Department of Science   Associate Professor

    2017.4 - 2024.3

  • Niigata University   Graduate School of Science and Technology Fundamental Sciences   Associate Professor

    2011.4

  • Niigata University   Graduate School of Science and Technology Fundamental Sciences   Associate Professor

    2011.4

  • Niigata University   Abolition organization Mathematical Analysis   Associate Professor

    2011.4 - 2017.3

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Committee Memberships

  • ICIAM2023 TOKYO (10th International Congress on Industrial and Applied Mathematics)   Local Scientific Program Commitee  

    2022.1 - 2023.8   

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  • 日本数学会   応用数学分科会 分科会委員  

    2017.10 - 2019.9   

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    Committee type:Academic society

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Papers

  • K7-minors in optimal 1-embedded graphs on the projective plane

    Katsuya Sone, Yusuke Suzuki

    Discrete Mathematics   2024.9

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    DOI: 10.1016/j.disc.2024.114074

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  • Partially broken orientations of Eulerian graphs on closed surfaces Reviewed

    Atsuhiro Nakamoto, Yusuke Suzuki

    Discrete Mathematics   2024.7

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    Authorship:Lead author   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.disc.2024.114016

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  • Optimal 1-planar multigraphs Reviewed

    Katsuya Sone, Yusuke Suzuki

    Discrete Mathematics   2023.10

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    Authorship:Lead author   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.disc.2023.113553

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  • Q4-irreducible even triangulations of the projective plane Reviewed

    Jun Hasegawa, Yusuke Suzuki

    Discrete Mathematics   345 ( 3 )   112736 - 112736   2022.3

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Elsevier BV  

    DOI: 10.1016/j.disc.2021.112736

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  • 1-Embeddability of complete multipartite graphs on the projective plane Reviewed

    Hikari Shibuya, Yusuke Suzuki

    Discrete Mathematics   344 ( 9 )   112518 - 112518   2021.9

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Elsevier BV  

    DOI: 10.1016/j.disc.2021.112518

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  • Non 1-planarity of lexicographic products of graphs Reviewed

    Naoki Matsumoto, Yusuke Suzuki

    Discussiones Mathematicae Graph Theory   41 ( 4 )   1103 - 1114   2021

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora  

    DOI: 10.7151/dmgt.2231

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  • Partially Broken Orientations of Eulerian Plane Graphs Reviewed

    Gen Kawatani, Yusuke Suzuki

    Graphs and Combinatorics   36 ( 3 )   767 - 777   2020.5

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media {LLC}  

    DOI: 10.1007/s00373-020-02152-1

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    Other Link: http://link.springer.com/article/10.1007/s00373-020-02152-1/fulltext.html

  • Rhombus Tilings of an Even-Sided Polygon and Quadrangulations on the Projective Plane Reviewed

    Hiroaki Hamanaka, Atsuhiro Nakamoto, Yusuke Suzuki

    Graphs and Combinatorics   36 ( 3 )   561 - 571   2020.5

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    DOI: 10.1007/s00373-020-02137-0

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    Other Link: http://link.springer.com/article/10.1007/s00373-020-02137-0/fulltext.html

  • Exceptional Balanced Triangulations on Surfaces Reviewed

    Steven Klee, Satoshi Murai, Yusuke Suzuki

    Graphs and Combinatorics   35 ( 6 )   1361 - 1373   2019.11

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media {LLC}  

    DOI: 10.1007/s00373-018-2001-x

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  • Generating Polyhedral Quadrangulations of the Projective Plane Reviewed

    Y. Suzuki

    ARS MATHEMATICA CONTEMPORANEA   19   153 - 183   2019

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  • The extendability of optimal 1-planar graphs Reviewed

    J.Fujisawa, K.Segawa, Y.Suzuki

    Graphs and Combinatorics   34   1089 - 1099   2018

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    DOI: 10.1007/s00373-018-1932-6

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  • No optimal 1-planar graph triangulates any non-orientable closed surface Reviewed

    T.Nagasawa, K.Noguchi, Y.Suzuki

    Journal of Graph Theory   89   350 - 360   2018

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1002/jgt.22255

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  • 1-embedded graphs which triangulate other surfaces Reviewed

    T. Nagasawa, K. Noguchi, Y. Suzuki

    J. Nonlinear Convex Anal.   19   1759 - 1770   2018

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  • Balanced subdivisions and flips on surfaces Reviewed

    Satoshi Murai, Yusuke Suzuki

    Proceedings of the American Mathematical Society   146 ( 3 )   939 - 951   2018

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:American Mathematical Society  

    In this paper, we show that two balanced triangulations of a closed surface are not necessarily connected by a sequence of balanced stellar subdivisions and welds. This answers a question posed by Izmestiev, Klee and Novik. We also show that two balanced triangulations of a closed surface are connected by a sequence of three local operations, which we call the pentagon contraction, the balanced edge subdivision and the balanced edge weld. In addition, we prove that two balanced triangulations of the 2-sphere are connected by a sequence of pentagon contractions and their inverses if none of them are the octahedral sphere.

    DOI: 10.1090/proc/13775

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  • A generating theorem of simple even triangulations with a finitizable set of reductions Reviewed

    Makoto Nishina, Yusuke Suzuki

    DISCRETE MATHEMATICS   340 ( 10 )   2604 - 2613   2017.10

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

    We shall determine exactly two (P, Q)-irreducible even triangulations of the projective plane. This result is a new generating theorem of even triangulations of the projective plane, that is, every even triangulation of the projective plane can be obtained from one of those two (P, Q)-irreducible even triangulations by a sequence of two expansions called a P-expansion and a Q-expansion, which were used in Batagelj (1984, 1989), Drapal and Lisonek (2010). Furthermore, we prove that for any closed surface F-2 there are finitely many (P, Q)-irreducible even triangulations of F-2. (C) 2017 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.disc.2017.06.018

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  • K-7-minors in optimal 1-planar graphs Reviewed

    Yusuke Suzuki

    DISCRETE MATHEMATICS   340 ( 6 )   1227 - 1234   2017.6

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    We discuss the existence of minors of given graphs in optimal 1-planar graphs. As our first main result, we prove that for any graph H, there exists an optimal 1-planar graph which contains H as a topological minor. Next, we consider minors of complete graphs. It is easily obtained from Mader's result (Mader, 1968) that every optimal 1-planar graph has a K-6-minor. In the paper, we characterize optimal 1-planar graphs having no K-7-minor. (C) 2017 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.disc.2017.01.022

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  • Cube-contractions in 3-connected quadrangulations Reviewed

    Yusuke Suzuki

    ARS MATHEMATICA CONTEMPORANEA   10 ( 2 )   281 - 290   2016

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:UP FAMNIT  

    DOI: 10.26493/1855-3974.552.bf3

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  • LOOSENESS AND INDEPENDENCE NUMBER OF TRIANGULATIONS ON CLOSED SURFACES Reviewed

    Atsuhiro Nakamoto, Seiya Negami, Kyoji Ohba, Yusuke Suzuki

    DISCUSSIONES MATHEMATICAE GRAPH THEORY   36 ( 3 )   545 - 554   2016

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:UNIV ZIELONA GORA  

    The looseness of a triangulation G on a closed surface F-2, denoted by xi(G), is defined as the minimum number k such that for any surjection c : V(G) -> {1, 2, ..., k + 3}, there is a face uvw of G with c(u), c(v) and c(w) all distinct. We shall bound xi(G) for triangulations G on closed surfaces by the independence number of G denoted by a(G). In particular, for a triangulation G on the sphere, we havexi(G) <= 11 alpha(G) - 10/6and this bound is sharp. For a triangulation G on a non-spherical surface F-2, we havexi(G) <= 2 alpha(G)+ l(F-2) - 2,where l(F-2) = left perpendicular(2 - chi(F-2))/2right perpendicular with Euler characteristic chi(F-2).

    DOI: 10.7151/dmgt.1870

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  • Relationship Among Triangulations, Quadrangulations and Optimal 1-Planar Graphs Reviewed

    Kenta Noguchi, Yusuke Suzuki

    GRAPHS AND COMBINATORICS   31 ( 6 )   1965 - 1972   2015.11

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER JAPAN KK  

    In this paper, we examine relationship of graphs on surfaces: triangulations, quadrangulations and optimal -planar graphs. For a given quadrangulation of a closed surface can be extended to a triangulation by adding a diagonal edge in every face of . We show that every quadrangulation of with at least six vertices can be extended to a -connected triangulation. Moreover, we show that every -connected triangulation of has a -connected spanning quadrangulation subgraph. As corollaries of these results, we show that every optimal -planar graph has a -connected triangulation subgraph, and that every plane -connected triangulation can be extended to an optimal -planar graph by adding some edges.

    DOI: 10.1007/s00373-015-1568-8

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  • A Linear-Time Algorithm for Testing Outer-1-Planarity Reviewed

    Seok-Hee Hong, Peter Eades, Naoki Katoh, Giuseppe Liotta, Pascal Schweitzer, Yusuke Suzuki

    ALGORITHMICA   72 ( 4 )   1033 - 1054   2015.8

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    A graph is 1-planar if it can be embedded in the plane with at most one crossing per edge. It is known that the problem of testing 1-planarity of a graph is NP-complete. In this paper, we study outer-1-planar graphs. A graph is outer-1-planar if it has an embedding in which every vertex is on the outer face and each edge has at most one crossing. We present a linear time algorithm to test whether a given graph is outer-1-planar. The algorithm can be used to produce an outer-1-planar embedding in linear time if it exists.

    DOI: 10.1007/s00453-014-9890-8

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  • Generating 3-Connected Quadrangulations on Surfaces Reviewed

    Momoko Nagashima, Atsuhiro Nakamoto, Seiya Negami, Yusuke Suzuki

    ARS COMBINATORIA   116   371 - 384   2014.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:CHARLES BABBAGE RES CTR  

    Let G be a simple quadrangulation on a closed surface F-2. A face-contraction and a 4-cycle removal are two reductions for quadrangulations defined in this paper.
    G is irreducible if any face-contraction breaks the simplicity of G,
    G is D-3-irreducible if G has minimum degree at least 3 and any face-contraction or any 4-cycle removal either breaks the simplicity or reduces the minimum degree to less than 3,
    G is K-3-irreducible if G is 3-connected and any face-contraction or any 4-cycle removal breaks the simplicity or the 3-connectedness of the graph,
    G is S-4-irreducible if G has no separating 4-cycle and any face-contraction breaks the simplicity or creates a separating 4-cycle.
    In [7], it was shown that except the sphere and the projective plane, the irreducibility and the D-3-irreducibility of quadrangulations are equivalent. In this paper, we shall prove that for all surfaces, the D-3-irreducibility and the K-3-irreducibility of quadrangulations are equivalent. We also prove that for the sphere, the projective plane and the torus, the D-3-irreducibility and the S-4-irreducibility of quadrangulations are equivalent, but this does not hold for surfaces of high genus.

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  • 3-Polychromatic quadrangulations on surfaces Reviewed

    R.Mukae, A.Nakamoto, Y.Suzuki

    Congressus Numerantium   219   43 - 51   2014

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  • A linear time algorithm for testing maximal 1-planarity of graphs with a rotation system Reviewed

    Peter Eades, Seok-Hee Hong, Naoki Katoh, Giuseppe Liotta, Pascal Schweitzer, Yusuke Suzuki

    THEORETICAL COMPUTER SCIENCE   513   65 - 76   2013.11

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    A 1-planar graph is a graph that can be embedded in the plane with at most one crossing per edge. It is known that testing 1-planarity of a graph is NP-complete.
    In this paper, we consider maximal 1-planar graphs. A graph G is maximal 1-planar if addition of any edge destroys 1-planarity of G. We first study combinatorial properties of maximal 1-planar embeddings. In particular, we show that in a maximal 1-planar embedding, the graph induced by the non-crossing edges is spanning and biconnected.
    Using the properties, we show that the problem of testing maximal 1-planarity of a graph G can be solved in linear time, if a rotation system Phi (i.e., the circular ordering of edges for each vertex) is given. We also prove that there is at most one maximal 1-planar embedding xi of G that is consistent with the given rotation system Phi. Our algorithm also produces such an embedding in linear time, if it exists. (C) 2013 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.tcs.2013.09.029

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  • A linear-time algorithm for testing outer-1-planarity Reviewed

    Seok-Hee Hong, Peter Eades, Naoki Katoh, Giuseppe Liotta, Pascal Schweitzer, Yusuke Suzuki

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)   8242   71 - 82   2013

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    A graph is 1-planar if it can be embedded in the plane with at most one crossing per edge. A graph is outer-1-planar if it has an embedding in which every vertex is on the outer face and each edge has at most one crossing. We present a linear time algorithm to test whether a graph is outer-1-planar. The algorithm can be used to produce an outer-1-planar embedding in linear time if it exists. © 2013 Springer International Publishing Switzerland.

    DOI: 10.1007/978-3-319-03841-4-7

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  • Testing maximal 1-planarity of graphs with a rotation system in linear time (extended abstract) Reviewed

    Peter Eades, Seok-Hee Hong, Naoki Katoh, Giuseppe Liotta, Pascal Schweitzer, Yusuke Suzuki

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)   7704   339 - 345   2013

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    A 1-planar graph is a graph that can be embedded in the plane with at most one crossing per edge. It is known that testing 1-planarity of a graph is NP-complete. A 1-planar embedding of a graph G is maximal if no edge can be added without violating the 1-planarity of G. In this paper we show that the problem of testing maximal 1-planarity of a graph G can be solved in linear time, if a rotation system (i.e., the circular ordering of edges for each vertex) is given. We also prove that there is at most one maximal 1-planar embedding of G that preserves the given rotation system, and our algorithm produces such an embedding in linear time, if it exists. © 2013 Springer-Verlag.

    DOI: 10.1007/978-3-642-36763-2_30

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  • Coloring Eulerian Triangulations of the Klein Bottle Reviewed

    Daniel Kral, Bojan Mohar, Atsuhiro Nakamoto, Ondrej Pangrac, Yusuke Suzuki

    GRAPHS AND COMBINATORICS   28 ( 4 )   499 - 530   2012.7

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    We show that an Eulerian triangulation of the Klein bottle has chromatic number equal to six if and only if it contains a complete graph of order six, and it is 5-colorable, otherwise. As a consequence of our proof, we derive that every Eulerian triangulation of the Klein bottle with face-width at least four is 5-colorable.

    DOI: 10.1007/s00373-011-1063-9

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  • Y-Rotation in k-Minimal quadrangulations on the Projective Plane

    Atsuhiro Nakamoto, Yusuke Suzuki

    JOURNAL OF GRAPH THEORY   69 ( 3 )   301 - 313   2012.3

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:WILEY-BLACKWELL  

    Let G be a quadrangulation on a surface, and let f be a face bounded by a 4-cycle abcd. A face-contraction of f is to identify a and c (or b and d) to eliminate f. We say that a simple quadrangulation G on the surface is k-minimal if the length of a shortest essential cycle is k(>= 3), but any face-contraction in G breaks this property or the simplicity of the graph. In this article, we shall prove that for any fixed integer k >= 3, any two k-minimal quadrangulations on the projective plane can be transformed into each other by a sequence of Y-rotations of vertices of degree 3, where a Y-rotation of a vertex v of degree 3 is to remove three edges vv(1), vv(3), vv(5) in the hexagonal region consisting of three quadrilateral faces vv(1)v(2)v(3), vv(3)v(4)v(5), and vv(5)v(6)v(1), and to add three edges vv(2), vv(4), vv(6). Actually, every k-minimal quadrangulation (k >= 4) can be reduced to a (k-1)-minimal quadrangulation by the operation called Mobius contraction, which is mentioned in Lemma 13. (c) 2011 Wiley Periodicals, Inc. J Graph Theory 69: 301313, 2012

    DOI: 10.1002/jgt.20583

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  • ON PROPERTIES OF MAXIMAL 1-PLANAR GRAPHS Reviewed

    David Hudak, Tomas Madaras, Yusuke Suzuki

    DISCUSSIONES MATHEMATICAE GRAPH THEORY   32 ( 4 )   737 - 747   2012

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:UNIV ZIELONA GORA  

    A graph is called 1-planar if there exists a drawing in the plane so that each edge contains at most one crossing. We study maximal 1-planar graphs from the point of view of properties of their diagrams, local structure and hamiltonicity.

    DOI: 10.7151/dmgt.1639

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  • Re-Embedding Structures of 4-Connected Projective-Planar Graphs Reviewed

    Yusuke Suzuki

    JOURNAL OF GRAPH THEORY   68 ( 3 )   213 - 228   2011.11

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:WILEY-BLACKWELL  

    We identify the structures of 4-connected projective-planar graphs which generate their inequivalent embeddings on the projective plane, showing two series of graphs the number of whose inequivalent embeddings is held by O(n) with respect to the number of its vertices n. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 68: 213-228, 2011

    DOI: 10.1002/jgt.20553

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  • The 2-extendability of 5-connected graphs on surfaces with large representativity Reviewed

    Ken-ichi Kawarabayashi, Seiya Negami, Michael D. Plummer, Yusuke Suzuki

    JOURNAL OF COMBINATORIAL THEORY SERIES B   101 ( 4 )   206 - 213   2011.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    A graph with at least 2k + 2 vertices is said to be k-extendable if any independent set of k edges in it extends to a perfect matching. We shall show that every 5-connected graph G of even order embedded on a closed surface F(2), except the sphere, is 2-extendable if rho(G) &gt;= 7 - 2x (F(2)), where rho(G) stands for the representativity of G on F(2) and x (F(2)) for the Euler characteristic of F(2). (C) 2011 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jctb.2011.02.001

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  • The 2-extendability of 5-connected graphs on the Klein bottle Reviewed

    Seiya Negami, Yusuke Suzuki

    DISCRETE MATHEMATICS   310 ( 19 )   2510 - 2518   2010.10

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    A graph is said to be k-extendable if any independent set of k edges extends to a perfect matching. in this paper, we shall characterize the forbidden structures for 5-connected graphs on the Klein bottle to be 2-extendable. This fact also gives us a sharp lower bound of representativity of 5-connected graphs embedded on the Klein bottle to have such a property, which was considered in Kawarabayashi et al. (submitted for publication) [4]. (C) 2010 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.disc.2010.06.020

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  • The 2-Extendability of Graphs on the Projective Plane, the Torus and the Klein Bottle Reviewed

    Iwao Mizukai, Seiya Negami, Yusuke Suzuki

    GRAPHS AND COMBINATORICS   26 ( 4 )   549 - 557   2010.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER TOKYO  

    A graph is said to be k-extendable if any independent set of k edges extends to a perfect matching. We shall show that every 5-connected graph of even order embedded on the projective plane and every 6-connected one embedded on the torus and the Klein bottle is 2-extendable and characterize the forbidden structures for 5-connected toroidal graphs to be 2-extendable.

    DOI: 10.1007/s00373-010-0927-8

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  • K (6)-Minors in Triangulations on the Nonorientable Surface of Genus 3 Reviewed

    Raiji Mukae, Atsuhiro Nakamoto, Yoshiaki Oda, Yusuke Suzuki

    GRAPHS AND COMBINATORICS   26 ( 4 )   559 - 570   2010.7

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    In this paper, we shall give a constructive characterization of triangulations on the nonorientable surface of genus 3 without K (6)-minors. Our characterization implies that every 5-connected triangulation and every 4-representative triangulation on the surface has a K (6)-minor.

    DOI: 10.1007/s00373-010-0931-z

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  • Optimal 1-planar graphs which triangulate other surfaces Reviewed

    Yusuke Suzuki

    DISCRETE MATHEMATICS   310 ( 1 )   6 - 11   2010.1

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

    We show that, for any given non-spherical orientable closed surface F(2), there exists an optimal 1-planar graph which can be embedded on F(2) as a triangulation. On the other hand, we prove that there does not exist any such graph for the nonorientable closed surfaces of genus at most 3. (C) 2009 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.disc.2009.07.016

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  • No optimal 1-planar graph triangulates the non-orientable closed surface of genus 4 Reviewed

    K. Ishiguro, S. Negami, Y. Suzuki, K. Yamamoto

    Congress numerantium   202   25 - 31   2010

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  • Diagonal slides and diagonal rotations in quadrangulations on the sphere Reviewed

    A.Nakamoto, Y.Suzuki

    Yokohama Mathematical Journal   55 ( 2 )   105 - 112   2010

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Yokohama City Unicersity and Yokohama National University  

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  • Diagonal slides and diagonal rotations in quadrangulations on the sphere Reviewed

    A. Nakamoto, Y. Suzuki

    Yokohama mathematical journal   55 ( 2 )   105 - 112   2010

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Yokohama City Unicersity and Yokohama National University  

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  • RE-EMBEDDINGS OF MAXIMUM 1-PLANAR GRAPHS Reviewed

    Yusuke Suzuki

    SIAM JOURNAL ON DISCRETE MATHEMATICS   24 ( 4 )   1527 - 1540   2010

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SIAM PUBLICATIONS  

    In this paper, we examine the re-embeddability of maximum 1-planar graphs. In particular, we prove that every optimal 1-planar graph is uniquely 1-embeddable on the sphere except for a sequence of graphs that are minimal with respect to certain reductions. These optimal 1-planar graphs are closely related to their quadrangular subgraphs. We also give a generating theorem for optimal 1-planar graphs.

    DOI: 10.1137/090746835

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  • N-flips in even triangulations on surfaces Reviewed

    Ken-ichi Kawarabayashi, Atsuhiro Nakamoto, Yusuke Suzuki

    JOURNAL OF COMBINATORIAL THEORY SERIES B   99 ( 1 )   229 - 246   2009.1

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    In this paper, we show that any two even triangulations Oil the same closed Surface with the same and sufficiently large number of vertices can be transformed into each other by a sequence of two specifically defined deformations called an N-flip and a P(2)-fliP, up to homeomorphism, if they have the same homological structure. (C) 2008 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jctb.2008.06.006

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  • N-flips in even triangulations on the projective plane Reviewed

    Atsuhiro Nakamoto, Yusuke Suzuki

    DISCRETE MATHEMATICS   308 ( 23 )   5454 - 5462   2008.12

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    We shall show that any two even triangulations G and G' on the projective plane with vertical bar V(G)vertical bar = vertical bar V(G')vertical bar >= 14 can be transformed into each other by two operations called an N-flip and P-2-flip, if and only if both of them are simultaneously 3-colorable, or not. (C) 2007 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.disc.2007.10.015

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  • N-Flips in even triangulations on surfaces Reviewed

    Ken-ichi Kawarabayashi, Atsuhiro Nakamoto, Yusuke Suzuki

    Electronic Notes in Discrete Mathematics   31 ( C )   99 - 104   2008.8

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    In this paper, we show that any two even triangulations on the same closed surface with the same and sufficiently large number of vertices can be transformed into each other by a sequence of two specifically defined deformations called an N-flip and a P2-flip, up to homeomorphism, if they have the same homological structure. © 2008 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.endm.2008.06.020

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  • Generating even triangulations of the projective plane Reviewed

    Yusuke Suzuki, Takahiro Watanabe

    JOURNAL OF GRAPH THEORY   56 ( 4 )   333 - 349   2007.12

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    We shall determine the 20 families of irreducible even triangulations of the projective plane. Every even triangulation of the projective plane can be obtained from one of them by a sequence of even-splittings and attaching octahedra, both of which were first given by Batagelj [2]. (c) 2007 Wiley Periodicals, Inc.

    DOI: 10.1002/jgt.20269

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  • Graphs that triangulate a given surface and quadrangulate another surface Reviewed

    Yusuke Suzuki

    JOURNAL OF COMBINATORIAL THEORY SERIES B   97 ( 2 )   237 - 244   2007.3

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    We show that for any closed surface F with chi(F) &lt;= -4 (or chi(F) &lt;= -2), there exist graphs that triangulate the torus or the Klein bottle (or the projective plane) and that quadrangulate F. We also give a sufficient condition for a graph triangulating a closed surface to quadrangulate some other surface. (c) 2006 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jctb.2006.05.005

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  • N-flips in even triangulations on the sphere Reviewed

    A Nakamoto, T Sakuma, Y Suzuki

    JOURNAL OF GRAPH THEORY   51 ( 3 )   260 - 268   2006.3

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    A triangulation is said to be even if each vertex has even degree. For even triangulations, define the N-flip and the P-2-flip as two deformations preserving the number of vertices. We shall prove that any two even triangulations on the sphere with the same number of vertices can be transformed into each other by a sequence of N- and P-2-flips. (c) 2005 Wiley Periodicals, Inc.

    DOI: 10.1002/jgt.20132

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  • Triangulations on closed surfaces which quadrangulate other surfaces II Reviewed

    Y Suzuki

    DISCRETE MATHEMATICS   303 ( 1-3 )   234 - 242   2005.11

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    It has already been proved that given two closed surfaces F-1(2) and F-2(2) with 2 chi(F-1(2))-chi((2)(F)2) &gt;= 4, there exists a triangulation on F-1(2) which can be embedded on F-2(2) as a quadrangulation. In this paper we refine that result, showing that there exists an integer go such that for any two closed surfaces with genus g(1) &gt;= g(0) and genus g(2) satisfying 2 chi(F-1(2))-chi(F-2(2)) &gt;= O(g(1)), there exists a triangulation of the first surface which can be re-embedded on the second as a quadrangulation. Moreover, on the right-hand side of the inequality, we obtain a concrete expression which is asymptotically O (g(1)). We also obtain similar results for non-orientable surfaces. (c) 2005 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.disc.2004.12.025

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  • Re-embeddability of graphs on surfaces

    鈴木有祐

    2004.3

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  • Projective-planar double coverings of 3-connected graphs Reviewed

    S.Negami, Y.Suzuki

    Yokohama Mathematical Journal   50 ( 1 )   87 - 95   2003

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    CiNii Article

    CiNii Books

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  • 5-Connected planar triangulations quadrangulating other surfaces Reviewed

    S.Negami, Y.Suzuki

    Yokohama Mathematical Journal   47   187 - 193   2000

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Books

  • Beyond Planar Graphs

    S.~Hong, T.~Tokuyama Eds( Role: Joint author ,  Chapter 4 1-planar graph (p47--p68))

    Springer Singapore  2020 

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Presentations

  • Partially broken orientations of Eulerian graphs on closed surfaces

    2022.8 

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  • 四角形分割における頂点数の増減のある局所変形問題について

    鈴木 有祐

    第33回位相幾何学的グラフ理論研究集会  2021.11 

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  • 二部グラフ的及び三部グラフ的1-交差埋め込みの辺数の上界について

    鈴木 有祐

    日本数学会年会(Zoomウェビナーによるオンライン講演)  2021.3 

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  • 二部グラフ的及び三部グラフ的1-交差埋め込みの辺数の上界について

    鈴木 有祐

    第32回位相幾何学的グラフ理論研究集会(オンラインによる講演)  2020.11 

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  • Orientations of Eulerian graphs on the plane

    YNU-PSU Joint Mathematical Seminar 2020  2020.2 

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  • グラフの辞書式積の非1-平面性について

    鈴木 有祐

    第31回位相幾何学的グラフ理論研究集会  2019.11 

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  • グラフの辞書式積の非1-平面性について

    鈴木 有祐

    日本数学秋季総合分科会  2019.9 

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  • Non-1-planarity of lexicographic products of graphs International conference

    Y. Suzuki

    28th Workshop Cycle and Colorings  2019.9 

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  • Partially broken orientations of Eulerian plane graphs International conference

    Y. Suzuki

    8th Slovenian International Conference on Graph Theory  2019.6 

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  • Partially broken orientations of Eulerian plane graphs

    SUZUKI Yusuke

    2019.3 

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  • Partially broken orientations of Eulerian plane graphs International conference

    Y. Suzuki

    6th Pacific Workshop on Discrete Mathematics  2018.11 

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  • Partially broken orientations of Eulerian plane graphs International conference

    Y. Suzuki

    30th Workshop on topological graph theory  2018.10 

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    Venue:Hatoba Hall(Yokohama), Japan  

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  • Exceptional balanced triangulations on surfaces International conference

    Y. Suzuki

    The Japanese Conference on Combinatorics and its Applications  2018.5 

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    Venue:Sendai International Center, Japan  

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  • The Second Japan-Sino Symposium on Graph Theory

    鈴木有祐

    2018.3 

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    Venue:東京大学駒場キャンパス  

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  • 例外的$3$-染色的三角形分割について

    鈴木有祐

    第29回位相幾何学的グラフ理論研究集会  2017.11 

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:横浜国立大学 みなとみらいキャンパス  

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  • Balanced subdivisions and flips on surfaces

    鈴木有祐

    Japanese Conference on Combinatorics and its Applications・ 離散数学とその応用研究集会2017  2017.8 

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:熊本大学  

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  • Balanced subdivisions and flips on surfaces International conference

    Y. Suzuki

    The Seventh Workshop Graph Embeddings and Maps on Surfaces  2017.7 

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    Venue:Grand Hotel Permon, Podbansk\'{e}, Slovakia  

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  • $K_6$-Minors in triangulations on the nonorientable surface of genus $4$

    鈴木有祐

    位相幾何学的グラフ理論セミナー  2017.6 

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    Venue:横浜国立大学  

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  • A generating theorem of simple even triangulations with a finitizable International conference

    Y. Suzuki

    International Workshop on Combinatorial and Computational Aspects of Optimization, Topology and Algebra (ACCOTA 2016)  2016.11 

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    Venue:Holiday Inn Resort Los Cabos, Mexico  

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  • $3$-染色的三角形分割に対する変形操作について

    鈴木有祐

    第28回位相幾何学的グラフ理論研究集会  2016.11 

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    Venue:情報科学専門学校(岩崎学園)  

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  • 再埋蔵的視点から見たグラフの1-交差埋め込み Invited

    鈴木有祐

    最適化の基盤とフロンティア研究部会 第8回研究会  2016.10 

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    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:新潟大学  

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  • $3$-染色的三角形分割に対する変形操作について

    鈴木有祐

    離散数学とその応用研究集会2016  2016.8 

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:高城コミュニティーセンター  

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  • set of reductions International conference

    Y. Suzuki

    The Fifth Asian Conference on Nonlinear Analysis and Optimization  2016.8 

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    Venue:Toki Messe, Niigata  

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  • 最適$1$-交差埋め込みの$K_7$-マイナーについて

    鈴木有祐

    第27回位相幾何学的グラフ理論研究集会  2015.11 

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    Venue:横浜国立大学  

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  • $K_7$-Minors in optimal $1$-planar graphs International conference

    Y. Suzuki

    The Second Japan-Sino Symposium on Graph Theory,  2015.11 

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    Venue:Morito Memorial Hall(Tokyo University of Science)  

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  • Recent works on optimal $1$-planar graphs Invited International conference

    Y. Suzuki

    The 9th KIAS Combinatorics Workshop  2015.9 

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    Venue:Broom Vista (Korea)  

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  • $K_7$-Minors in optimal $1$-planar graphs

    鈴木有祐

    離散数学とその応用研究集会2015  2015.8 

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    Venue:熊本大学工学部百周年記念館  

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  • $K_7$-Minors in optimal $1$-planar graphs International conference

    Y. Suzuki

    Combinatorics and Their Applications  2015.6 

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    Venue:Ramada Resort (Kranjska Gora, Slovenia)  

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  • 多面体的四角形分割に対する縮小操作について

    鈴木有祐

    日本数学会2014年度会  2014.3 

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    Venue:学習院大学  

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  • 閉曲面上のグラフの生成定理について Invited

    鈴木有祐

    第10回組合せ論若手研究集会  2014.2 

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    Venue:慶應大学  

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  • 多面体的四角形分割に対する減少操作について

    鈴木有祐

    応用数学合同研究集会  2013.12 

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:龍谷大学  

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  • Cube-contractions in 3-connected quadrangulations International conference

    Y. Suzuki

    The 25th Workshop on Topological Graph Theory in Yokohama  2013.11 

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    Venue:Yokohama National University  

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  • Cube-contractions in 3-connected quadrangulations

    鈴木有祐

    離散数学とその応用研究集会2013  2013.8 

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    Venue:山形市保健センター・視聴覚室  

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  • Cube-contractions in 3-connected quadrangulations on surfaces International conference

    Y. Suzuki

    The Sixth Workshop Graph Embeddings and Maps on Surfaces  2013.7 

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    Venue:Smolenice castle, Slovakia  

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  • 多面体的四角形分割に対する縮小操作について International conference

    鈴木有祐

    日本数学会2014年度会  2013.3 

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    Venue:学習院大学  

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  • 再埋蔵的視点から見たグラフの1-交差埋め込み

    鈴木 有祐

    日本数学会・秋季総合分科会  2012.9 

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    Venue:九州大学  

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  • The number of edges of maximal 1-planar

    鈴木 有祐

    渡辺守先生ご退職記念関西グラフ理論研究集会  2012.3 

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    Venue:加計国際学術交流センター  

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  • Re-embeddings of optimal 1-embeddings of the projective plane

    鈴木 有祐

    応用数学合同研究集会  2011.12 

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    Venue:龍谷大学  

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  • 射影平面上の optimal 1-embedding の再埋蔵について

    鈴木 有祐

    離散数学とその応用研究集会2011  2011.8 

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    Venue:奈良県文化会館  

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  • Optimal 1-embedding の再埋蔵列挙プログラムについて

    鈴木 有祐

    第22回位相幾何学的グラフ理論研究集会  2010.11 

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    Venue:横浜国立大学  

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  • Generating polyhedral quadrangulations of the projective plane International conference

    Suzuki Yusuke

    Sixth Cracow Conference on Graph theory ``ZGORZELISKO'10''  2010.9 

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    Venue:Hotel Tatry, Poland  

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  • On properties of maximal 1-planar graphs

    鈴木 有祐

    日本数学会・秋季総合分科会  2010.9 

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    Venue:名古屋大学  

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  • Generating polyhedral quadrangulations

    鈴木 有祐

    離散数学とその応用研究集会2010  2010.3 

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    Venue:高知大学朝倉キャンパス  

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  • On properties of maximal 1-planar graphs International conference

    鈴木 有祐

    岡村治子先生退職記念研究集会  2010.3 

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    Venue:甲南大学  

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  • Re-embeddings of maximum 1-planar graphs International conference

    Suzuki Yusuke

    33rd Australasian Conference on  2009.12 

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    Venue:The University of Newcastle  

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  • Maximum 1-planar graph の再埋蔵について

    鈴木 有祐

    第21回位相幾何学的グラフ理論研究集会  2009.11 

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    Venue:横浜国立大学  

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  • Generation of quadrangulations with some conditions

    鈴木 有祐

    離散幾何とその応用研究集会2009  2009.8 

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    Venue:茨城大学工学部日立キャンパス  

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  • Generation of quadrangulations on surfaces International conference

    鈴木 有祐

    離散幾何とグラフ理論1日研究集会  2009.5 

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    Venue:東海大学教育開発研究所  

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  • Edge-width k-minimal quadrangulation

    鈴木 有祐

    組合せ論・離散幾何研究集会2009  2009.3 

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    Venue:琉球大学研究者交流会館  

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  • Edge-width k-minimal quadrangulation の有限性について

    鈴木 有祐

    組み合わせ論若手研究集会  2009.2 

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    Venue:慶應義塾大学矢上キャンパス  

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  • Constructing 5-connected toroidal graphs which have many inequivalent embeddings

    鈴木 有祐

    応用数学合同研究集会  2008.12 

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    Venue:龍谷大学瀬田キャンパス  

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  • Optimal 1-planar graphs which triangulate other surfaces International conference

    Suzuki Yusuke

    The 20th Workshop on Topological Graph Theory  2008.11 

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    Venue:Yokohama National University  

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  • Optimal 1-planar graph (O1PG) の埋め込みの一意性について

    鈴木 有祐

    位相幾何学的グラフ理論セミナー  2008.10 

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:横浜国立大学  

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  • Y-rotations in k-minimal

    鈴木 有祐

    位相幾何学的グラフ理論セミナー  2008.10 

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    Venue:横浜国立大学  

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  • Uniqueness of embeddings of optimal 1-planar graphs

    鈴木 有祐

    2008年度 RIMS共同研究「次数条件と因子が支配するグラフの幾何と解析」  2008.9 

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    Venue:京都大学数理解析研究所  

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  • N-Flips in even triangulations on the sphere

    鈴木 有祐

    日本数学会・秋季総合分科会  2008.9 

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    Venue:東京工業大学  

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  • Optimal 1-planar graphs which triangulate other surfaces

    鈴木 有祐

    離散数学とその応用研究集会2008  2008.8 

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:茨城大学インフォメーションセンター  

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  • Uniqueness of embeddings of optimal 1-planar graphs

    鈴木 有祐

    純粋数学及び応用数学としての組合わせ論・離散数学そしてその周辺ワークショップ  2008.7 

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:東京電気通信大学  

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  • Edge-width $k$-minimal quadrangulation の有限性について

    鈴木 有祐

    位相幾何学的グラフ理論セミナー  2008.7 

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    Venue:横浜国立大学  

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  • N-flips in even triangulations on surfaces International conference

    Suzuki Yusuke

    Topological & Geometric Graph Theory  2008.5 

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    Venue:\'{E}cole Normale Su\'{p}erieure, Paris  

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  • 球面の偶三角形分割のN-変形の回数

    鈴木 有祐

    第19回位相幾何学的グラフ理論研究集会  2007.11 

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    Venue:横浜国立大学  

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  • N-flips in even triangulations on surfaces International conference

    Suzuki Yusuke

    Thirty-Eighth Southeastern International Conference on Combinatorics, Graph  2007.3 

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    Venue:Florida Atlantic University  

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  • 閉曲面の偶三角形分割のN-変形

    鈴木 有祐

    第18回位相幾何学的グラフ理論研究集会  2006.11 

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    Venue:横浜国立大学  

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  • N-flips in even triangulations on surfaces International conference

    Suzuki Yusuke

    International Workshop on Discrete Mathematics and its Applications  2006.8 

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    Venue:Ibaraki University  

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Research Projects

  • 閉曲面上のグラフの生成定理と局所変形理論の融合的研究

    Grant number:20K03714

    2020.4 - 2023.3

    System name:科学研究費助成事業 基盤研究(C)

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

    鈴木 有祐

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    Grant amount:\4160000 ( Direct Cost: \3200000 、 Indirect Cost:\960000 )

    閉曲面上に埋め込まれたグラフが3-連結かつ3-representativeという条件を満たすとき,そのグラフは多面体的であると呼ばれる.球面上の多面体的グラフとしては5個の正多面体が有名であり一般によく知られた図形である.(球面上では上記の“3-representative”という条件が定義できないため,単に3-連結なものを考えればよい.)球面上の3-連結グラフに関しては多くの議論が存在するが,一般的に“良い”埋め込みとされていながら他の閉曲面上の(三角形分割以外の)多面体的グラフに関する具体的な結果は少ない.そこで我々は,一般の閉曲面上の多面体的四角形分割に焦点を絞って研究を行い,既約なグラフを有限個にするための縮小操作を8個に特定した.今年度はこの議論に関する論文の最終的な確認及びまとめを行った.(グラフ理論の専門誌への掲載が決定している.)
    また,閉曲面上の四角形分割に正六面体グラフを張り合わせることでその表面に現れるグラフをもとのグラフから局所変形によって得られたものと考え,それらの変形で与えられた2つのグラフが互いに移り合うかどうかという問題を考えた.手始めに情報を収集してみると,既に海外の研究者による結果が存在するという事実がわかったが,この論文を注意深く読み進めると書かれている内容に誤りがあることがわかった.(論文の著者ともコンタクトを取りその事実を確認済みである.)我々は,その誤りを正し,また,これらの結果を一般の閉曲面上の多面体的四角形分割に拡張することに成功した.また,変形操作の必要性に関する議論も行った.この結果を国内で行われた研究集会で発表し,他の研究者から得た意見をもとに研究を継続している状況である.

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  • Maximal 1-embedding of graphs on surfaces

    2016.4 - 2020.3

    System name:Grants-in-Aid for Scientific Research

    Research category:Grant-in-Aid for Scientific Research(C)

    Awarding organization:Japan Society for the Promotion of Science

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    Grant type:Competitive

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  • Synthetic research on topological graph theory centered around re-embeddings of graphs

    Grant number:25287027

    2013.4 - 2017.3

    System name:Grants-in-Aid for Scientific Research

    Research category:Grant-in-Aid for Scientific Research (B)

    Awarding organization:Japan Society for the Promotion of Science

    NEGAMI Seiya, OTA Katsuhiro, SATO Iwao, SUZUKI Yusuke

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    Grant amount:\13780000 ( Direct Cost: \10600000 、 Indirect Cost:\3180000 )

    We carried out synthetic research on topological graph theory, binding many subjects with a viewpoint of “re-embedding of graphs”. Especially, we developed a theory called “panel structures” to describe the re-embedding structures of triangulations on closed surface, implemented the theory as a computer program and re-verified a known-result on the torus, using it. We investigated many properties of asymmetric colorings of graphs embedded on closed surfaces and those of a new devised coloring called “triad-colorings” of triangulations on closed surfaces.

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  • 再埋蔵的視点から見た閉曲面上のグラフの1-交差埋め込みに関する研究 基盤研究(C) 代表

    2012.4

    System name:科学研究費助成事業

    Research category:若手研究(B)

    Awarding organization:日本学術振興会

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    Grant type:Competitive

    本課題研究では,各辺,他の辺とたかだか1回のみ辺の公差を許した閉曲面上のグラフ(1-交差埋め込み)を研究対象とする.
    閉曲面上に辺の公差なく埋め込まれたグラフは一般的にグラフ・マイナー理論と相性がよく,従来の研究はこれらに依存するものがほとんどである.しかし,`埋め込み'の条件を多少緩和しただけである1-交差埋め込みはこれらの手法で扱えないクラスであることが知られており,そのコントロール方法は未だに未知な部分が多い.本研究においては,グラフの埋め込み方そのものから議論を行うことで(再埋蔵理論),1-交差埋め込みの構造を解明していく.

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  • 代数的不変量に着目した閉曲面上のグラフの変形に関する研究 若手研究(B) 代表

    2009.4 - 2011.3

    System name:科学研究費助成事業

    Research category:若手研究(B)

    Awarding organization:日本学術振興会

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    Grant type:Competitive

    近年,ナノテクノロジーの発展とともに,いわゆるフラーレンなどの特殊な
    構造を持った分子構造が注目されている.これらの多くは,閉曲面の三角形分割の双対として理解でき,私の専門分野である位相幾何学的グラフ理論との関連は深い.それらの「違い」や「近さ」を考える際,その構造を保存しつつ局所的な変形によって移りあうかどうかを考えることには大きな意味がある.
    一般の三角形分割の対角変形に関しては過去に十分な結果がなされているが,それらの正則性を保存するような変形に対しては未だにほとんど研究が進んでいない.私は,これまで継続してそのような変形に注目して研究を進めてきたが,その過程において,従来の組合せ的な考察のみでは区別できず,閉曲面の代数的性質と合わせて考えることではじめて分類できるものがあることがわかってきた.
    そのような見地から,本研究課題においては,閉曲面に埋め込まれたグラフとその曲面の代数構造との

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  • 平面グラフとネットワークの解析

    2009.4 - 2010.3

    System name:国立情報学研究所共同研究

    Awarding organization:その他省庁等

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    Grant type:Competitive

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Teaching Experience (researchmap)

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Teaching Experience

  • 台湾スプリングセミナー II

    2023
    Institution name:新潟大学

  • 台湾スプリングセミナー I

    2023
    Institution name:新潟大学

  • 数学の世界

    2023
    Institution name:新潟大学

  • 代数・幾何特別講義

    2023
    Institution name:新潟大学

  • 位相幾何学

    2021
    Institution name:新潟大学

  • 構造数理特別講義

    2021
    Institution name:新潟大学

  • 理学スタディ・スキルズ

    2021
    Institution name:新潟大学

  • 数学基礎演習a

    2020
    Institution name:新潟大学

  • 線形代数IA

    2020
    Institution name:新潟大学

  • 線形代数IB

    2020
    Institution name:新潟大学

  • 数学基礎演習b

    2020
    Institution name:新潟大学

  • 線形代数IIB

    2018
    Institution name:新潟大学

  • 代数・幾何学序論A

    2018
    Institution name:新潟大学

  • 理学スタディ・スキルズ

    2018
    -
    2021
    Institution name:新潟大学

  • 専門力アクティブ・ラーニング

    2018
    -
    2019
    Institution name:新潟大学

  • 離散数学B

    2017
    Institution name:新潟大学

  • 離散数学A

    2017
    Institution name:新潟大学

  • 数学基礎A1

    2017
    -
    2019
    Institution name:新潟大学

  • 数学基礎A2

    2017
    -
    2019
    Institution name:新潟大学

  • トポロジーA

    2017
    -
    2018
    Institution name:新潟大学

  • トポロジーB

    2017
    -
    2018
    Institution name:新潟大学

  • スタディ・スキルズ(数学・情報学習法)

    2015
    -
    2016
    Institution name:新潟大学

  • 情報基礎数学II

    2014
    -
    2018
    Institution name:新潟大学

  • 数理科学セミナーⅠ(数学)

    2014
    -
    2015
    Institution name:新潟大学

  • 数理物質科学特定研究Ⅰ(数学)

    2014
    -
    2015
    Institution name:新潟大学

  • 数理科学文献詳読Ⅰ(数学)

    2014
    -
    2015
    Institution name:新潟大学

  • 数理科学研究発表演習〔中間発表〕(数学)

    2014
    -
    2015
    Institution name:新潟大学

  • 数学講究

    2013
    Institution name:新潟大学

  • グラフとネットワーク理論

    2013
    -
    2015
    Institution name:新潟大学

  • 構造数理特別講義I

    2012
    -
    2015
    Institution name:新潟大学

  • 数理物質科学特定研究Ⅱ(数学)

    2012
    -
    2015
    Institution name:新潟大学

  • 数理科学セミナーⅡ(数学)

    2012
    -
    2015
    Institution name:新潟大学

  • 数理科学文献詳読Ⅱ(数学)

    2012
    -
    2015
    Institution name:新潟大学

  • 数学基礎B

    2012
    Institution name:新潟大学

  • 自然科学総論Ⅰ

    2012
    Institution name:新潟大学

  • 基礎数学B II

    2012
    Institution name:新潟大学

  • 線形代数II

    2012
    Institution name:新潟大学

  • 位相幾何学特論

    2011
    Institution name:新潟大学

  • 線形代数III

    2011
    -
    2017
    Institution name:新潟大学

  • 数学基礎A

    2011
    -
    2016
    Institution name:新潟大学

  • トポロジー

    2011
    -
    2016
    Institution name:新潟大学

  • スタディ・スキルズ(数学学習法)

    2011
    -
    2014
    Institution name:新潟大学

  • 位相幾何学

    2011
    -
    2014
    Institution name:新潟大学

  • 基礎数学演習I

    2011
    Institution name:新潟大学

  • 基礎ゼミIII

    2011
    Institution name:新潟大学

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