OTA Katsuhiro

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics ( Yagami )

Position

Professor

External Links

Career 【 Display / hide 】

  • 1989.04
    -
    1993.03

    慶應義塾大学（理工学部数理科学科） ,助手

  • 1993.04
    -
    1997.03

    慶應義塾大学（理工学部数理科学科） ,専任講師

  • 1993.04
    -
    2010.09

    明治大学理工学部（数学A，確率，線形代数など）, 非常勤講師

  • 1997.04
    -
    Present

    慶應義塾大学（理工学部数理科学科） ,助教授

  • 2011.04
    -
    2011.09

    明治大学理工学部　非常勤講師

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Academic Background 【 Display / hide 】

  • 1984.03

    The University of Tokyo, Faculty of Science, 情報科学科

    University, Graduated

  • 1986.03

    The University of Tokyo, Graduate School, Division of Science, 情報科学専門課程

    Graduate School, Completed, Master's course

  • 1989.03

    The University of Tokyo, Graduate School, Division of Science, 情報科学専門課程

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

  • 理学　, The University of Tokyo, 1989.03

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Research Areas 【 Display / hide 】

  • Natural Science / Basic mathematics

  • Natural Science / Applied mathematics and statistics

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Research Keywords 【 Display / hide 】

  • Graph Theory

  • Combinatorics

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Books 【 Display / hide 】

  • グラフ理論

    R. Diestel著, シュプリンガー・フェアラーク東京, 2000.10

    　View Summary

    根上生也との共訳

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Papers 【 Display / hide 】

  • New Invariants for Partitioning a Graph Into 2-Connected Subgraphs

    Furuya M., Kashima M., Ota K.

    Journal of Graph Theory 109 ( 4 ) 505 - 513 2025.08

    ISSN  03649024

    　View Summary

    Let (Formula presented.) be a graph of order (Formula presented.). For an integer (Formula presented.), a partition (Formula presented.) of (Formula presented.) is called a (Formula presented.) -proper partition of (Formula presented.) if every (Formula presented.) induces a (Formula presented.) -connected subgraph of (Formula presented.). This concept was introduced by Ferrara et al., and Borozan et al. gave minimum degree conditions for the existence of a (Formula presented.) -proper partition. In particular, when (Formula presented.), they proved that if (Formula presented.), then (Formula presented.) has a 2-proper partition (Formula presented.) with (Formula presented.). Later, Chen et al. extended the result by giving a minimum degree sum condition for the existence of a 2-proper partition. In this paper, we introduce two new invariants of graphs (Formula presented.) and (Formula presented.), which are defined from degree sum of particular independent sets. Our result is that if (Formula presented.), then with some exceptions, (Formula presented.) has a 2-proper partition (Formula presented.) with (Formula presented.). We completely determine exceptional graphs. This result implies both of results by Borozan et al. and by Chen et al. Moreover, we obtain a minimum degree product condition for the existence of a 2-proper partition as a corollary of our result.

  • Some conditions for hamiltonian cycles in 1-tough (K2 ∪ kK1)-free graphs

    Ota K., Sanka M.

    Discrete Mathematics 347 ( 3 )  2024.03

    ISSN  0012365X

    　View Summary

    Let k≥2 be an integer. We say that a graph G is (K<inf>2</inf>∪kK<inf>1</inf>)-free if it does not contain K<inf>2</inf>∪kK<inf>1</inf> as an induced subgraph. Recently, Shi and Shan conjectured that every 1-tough and 2k-connected (K<inf>2</inf>∪kK<inf>1</inf>)-free graph is hamiltonian. In this paper, we solve this conjecture by proving that every 1-tough and k-connected (K<inf>2</inf>∪kK<inf>1</inf>)-free graph with minimum degree at least [Formula presented] is hamiltonian or the Petersen graph.

  • Minimum degree conditions for the existence of a sequence of cycles whose lengths differ by one or two

    Chiba S., Ota K., Yamashita T.

    Journal of Graph Theory 103 ( 2 ) 340 - 358 2023.06

    ISSN  03649024

    　View Summary

    Gao, Huo, Liu, and Ma proved a result on the existence of paths connecting specified two vertices whose lengths differ by one or two. By using this result, they settled two famous conjectures due to Thomassen. In this paper, we improve their result, and obtain a generalization of a result of Bondy and Vince.

  • Graph grabbing game on totally-weighted graphs

    Matsumoto N., Moriyama R., Ota K.

    Discrete Applied Mathematics 322   384 - 390 2022.12

    ISSN  0166218X

    　View Summary

    The graph grabbing game is a two-player game on a connected graph with a vertex-weight function. In the game, they alternately remove a non-cut vertex from the graph (i.e., the resulting graph remains connected) and get the weight assigned to the vertex. Each player's aim is to maximize his or her outcome, when all vertices have been taken. In this paper, we consider the graph grabbing game on totally-weighted graphs that are graphs with weight functions from a set of elements in the vertex set and the edge set to non-negative real numbers. In this version, when a player removes a non-cut vertex v, that player gets the weight of v plus the total weight assigned to the edges incident to v. In particular, we give some results of interest for the graph grabbing game on edge-weighted trees, i.e., every vertex has weight zero. Moreover, we consider the game on edge-weighed graphs in the altered rule that each player must keep the connectedness of graphs induced by edges.

  • Hamiltonian cycles in 2-tough 2K2-free graphs

    Ota K., Sanka M.

    Journal of Graph Theory 101 ( 4 ) 769 - 781 2022.12

    ISSN  03649024

    　View Summary

    A graph (Formula presented.) is called a (Formula presented.) -free graph if it does not contain (Formula presented.) as an induced subgraph. In 2014, Broersma, Patel, and Pyatkin showed that every 25-tough (Formula presented.) -free graph on at least three vertices is Hamiltonian. Recently, Shan improved this result by showing that 3-tough is sufficient instead of 25-tough. In this paper, we show that every 2-tough (Formula presented.) -free graph on at least three vertices is Hamiltonian, which was conjectured by Gao and Pasechnik.

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Reviews, Commentaries, etc. 【 Display / hide 】

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Presentations 【 Display / hide 】

  • Small theta subgraphs in sparse graphs

    [International presentation]  2017 Joint Mathematical Meetings, AMS Special Session on Topics in Graph Theory (Atlanta, Georgia, USA) , 

    2017.01
    , 

    Oral presentation (general)

  • Vertex-disjoint even cycles of the same length

    Y. Egawa, S. Fujita, K. Ota, T. Sakuma

    [International presentation]  ACCOTA 2016, International Workshop on Combinatorial and Computational Aspects of Optimization, Topology and Algebra (Los Cabos, Mexico) , 

    2016.11
    , 

    Oral presentation (general)

  • グラフが同じ長さの点素な偶閉路を含むための次数条件

    太田克弘, 江川嘉美, 藤田慎也, 佐久間雅

    [Domestic presentation]  日本数学会2015年度秋季総合分科会 (京都産業大学) , 

    2015.09
    , 

    Oral presentation (general), 日本数学会

  • Vertex-disjoint isomorphic theta subgraphs

    S. Fujita, K. Ota, T. Sakuma

    [International presentation]  2014 SIAM Conference on Discrete Mathematics, Minisymposium: Cycles and Paths (Minneaoplis, Minesota) , 

    2014.06
    , 

    Oral presentation (general)

  • Vertex-disjoint isomorphic theta subgraphs

    S. Fujita, K. Ota, T. Sakuma

    [International presentation]  The 3rd Taiwan-Japan Conference on Combinatorics and its Applications (National Chiayi University, Taiwan) , 

    2014.03
    , 

    Oral presentation (general)

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • グラフの大域構造に着目した極値問題の研究

    2022.04
    -
    2026.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 基盤研究(C), Principal investigator

  • 疎なグラフに対する極値グラフ理論の展開

    2016.04
    -
    2020.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Principal investigator

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Works 【 Display / hide 】

  • 理工学部１年生授業科目「数学２・数学４」の講義テキストの作成

    OTA KATSUHIRO

    2014.04
    -
    2015.03
    , 

    Other, Joint

  • 数理科学科２年生授業科目「数理科学基礎第２」の講義テキスト・演習問題の作成

    OTA KATSUHIRO

    2003.09
    -
    2005.02
    , 

    Other, Joint

  • 理工学部１年生授業科目「数学Ａ１，Ｂ１」の講義テキストの作成

    OTA KATSUHIRO

    　
    , 

    Other, Joint

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Courses Taught 【 Display / hide 】

  • MATHEMATICS 2B

    2025

  • MATHEMATICS 2A

    2025

  • INDEPENDENT STUDY ON FUNDAMENTAL SCIENCE AND TECHNOLOGY

    2025

  • GRADUATE RESEARCH ON FUNDAMENTAL SCIENCE AND TECHNOLOGY 2

    2025

  • GRADUATE RESEARCH ON FUNDAMENTAL SCIENCE AND TECHNOLOGY 1

    2025

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Memberships in Academic Societies 【 Display / hide 】

  • 日本数学会, 

    1986
    -
    Present

  • 日本数学会, 

    2004.10
    -
    2006.09

  • 日本数学会, 

    2010.06
    -
    2014.05

  • 日本数学会, 

    2008.06
    -
    2010.05
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Committee Experiences 【 Display / hide 】

  • 2004.10
    -
    2006.09

    Committee Member, 日本数学会

  • 2010.06
    -
    2014.05

    広報委員長, 日本数学会

  • 2008.06
    -
    2010.05

    広報委員会委員, 日本数学会

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