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2011 Fiscal Year Final Research Report

Structures of graphs on surfaces with complete minors

Research Project

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Project/Area Number 21540119
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionYokohama National University

Principal Investigator

NAKAMOTO Atsuhiro  横浜国立大学, 環境情報研究院, 准教授 (20314445)

Project Period (FY) 2009 – 2011
Keywords離散数学 / 位相幾何学的グラフ理論
Research Abstract

This study deals with a problem : A given graph G on a fixed surface, which complete graph Kn does G have as a minor? This problem is difficult in general, and the problem combining this and graph coloring is well-known as Hadwiger's conjecture, one of the important open problems in the literature. In the research, restricting graphs on surfaces to be triangulations, we characterized the graphs on the orientable surface of genus up to 3 and the nonorientable surface of genus up to 4 containing K_6 as a minor. In order to do so, we used the complete list of irreducible triangulations on those surfaces and the theory for graph transformations.

  • Research Products

    (34 results)

All 2012 2011 2010 2009 Other

All Journal Article (9 results) Presentation (24 results) Remarks (1 results)

  • [Journal Article] N-Flips in even triangulations and Dehn twists on the torus2011

    • Author(s)
      Y. Higuchi, A. Nakamoto, K. Ota and T.
    • Journal Title

      Discrete Math

      Pages: 1128-1135

  • [Journal Article] K6-Minors in triangulations on the nonorientable surface of genus 32010

    • Author(s)
      R. Mukae, A. Nakamoto, Y. Oda and Y. Suzuki
    • Journal Title

      Graphs Combin

      Pages: 559-570

  • [Journal Article] Diagonal flips in quad rangulations on the sphere.2010

    • Author(s)
      A. Nakamoto and Y. Suzuki
    • Journal Title

      Yokohama Math. J

      Pages: 105-112

  • [Journal Article] Dominating sets in triangulations on surfaces2010

    • Author(s)
      K. Kawarabayashi, T. Honjo and A. Nakamoto.
    • Journal Title

      J. Graph Theory

      Pages: 17-30

  • [Journal Article] An alternative enumeration of self complementary graphs2009

    • Author(s)
      A. Nakamoto, T. Shirakura and S. Tazawa.
    • Journal Title

      Util. Math

      Pages: 25-32

  • [Journal Article] Chromatic numbers of 6-regular graphs on the Klein bottle2009

    • Author(s)
      A. Nakamoto and N. Sasanuma.
    • Journal Title

      Austral as. J. Combin

      Pages: 73-85

  • [Journal Article] 3-trees with a few vertices of degree 3 in 3-connected planar graphs2009

    • Author(s)
      A. Nakamoto, K. Ota and Y. Oda.
    • Journal Title

      Discrete Math

      Pages: 666-672

  • [Journal Article] K6-Minors in triangulations and complete quad rangulations2009

    • Author(s)
      R. Mukae and A. Nakamoto.
    • Journal Title

      J. Graph Theory

      Pages: 302-312

  • [Journal Article] N-Flips in even triangulations on surfaces2009

    • Author(s)
      K. Kawarabayashi, A. Nakamoto and Y. Suzuki
    • Journal Title

      J. Combin. Theory, Ser. B

      Pages: 229-246

  • [Presentation] トーラスの直交分割について2012

    • Author(s)
      中本敦浩
    • Organizer
      渡辺守先生退職記念関西グラフ理論研究集会
    • Place of Presentation
      加計国際学術交流センター
    • Year and Date
      2012-03-08
  • [Presentation] 「曲面上のグラフの彩色について」,「曲面上のグラフの幾何学的実現について」2012

    • Author(s)
      中本敦浩
    • Organizer
      研究集会「直観幾何学」
    • Place of Presentation
      熊本大学
    • Year and Date
      2012-02-11
  • [Presentation] Colored quadrangulations with Steiner points2011

    • Author(s)
      A. Nakamoto
    • Organizer
      2011年応用数学合同研究集会
    • Place of Presentation
      龍谷大学瀬田キャンパス
    • Year and Date
      2011-12-16
  • [Presentation] Polychromatic coloring of cubic bipartite plane graphs2011

    • Author(s)
      A. Nakamoto
    • Organizer
      The 35th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing
    • Place of Presentation
      Monash University
    • Year and Date
      2011-12-08
  • [Presentation] Odd complete minors in even embeddings and their cycle parities2011

    • Author(s)
      中本敦浩
    • Organizer
      第23回位相幾何学的グラフ理論研究集会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2011-11-26
  • [Presentation] 3-正則平面2部グラフの多色4-彩色について2011

    • Author(s)
      中本敦浩
    • Organizer
      日本数学会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-29
  • [Presentation] A linear number of diagonal flips in triangulations on surfaces2011

    • Author(s)
      A. Nakamoto
    • Organizer
      EuroComb' 11, Renyi Institute
    • Place of Presentation
      Hungary
    • Year and Date
      2011-07-31
  • [Presentation] 3-正則平面2部グラフの多色4-彩色について2011

    • Author(s)
      中本敦浩
    • Organizer
      離散数学とその応用研究集会2011
    • Place of Presentation
      奈良県婦人会館
    • Year and Date
      2011-07-31
  • [Presentation] Quadrangulations on 3-colored point sets with Steiner points2011

    • Author(s)
      A. Nakamoto
    • Organizer
      XIV Spanish Meeting on Computational Geometry
    • Place of Presentation
      Spain
    • Year and Date
      2011-06-28
  • [Presentation] Quadrangulations on 3-colored point sets with Steiner points2011

    • Author(s)
      A. Nakamoto
    • Organizer
      7th Slovenian International Conference on Graph Theory
    • Place of Presentation
      Kompas Hotel, Slovenia
    • Year and Date
      2011-06-23
  • [Presentation] Odd minors in even embedding on surfaces2010

    • Author(s)
      中本敦浩
    • Organizer
      2010年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学瀬田キャンパス
    • Year and Date
      2010-12-15
  • [Presentation] Hamiltonian cycles in bipartite toroidal graphs with partite set of degree four vertices2010

    • Author(s)
      A. Nakamoto
    • Organizer
      The 3rd Pacific Workshop on Discrete Mathematics
    • Place of Presentation
      Tokai University Pacific center Honolulu
    • Year and Date
      2010-12-10
  • [Presentation] Y-Rotations in k-minimal quadrangulations on the projective plane2010

    • Author(s)
      A. Nakamoto
    • Organizer
      ACCOTA 2010
    • Place of Presentation
      Mexico
    • Year and Date
      2010-11-25
  • [Presentation] Hamiltonian cycles in bipartite toroidal graphs with partite set of degree four vertices2010

    • Author(s)
      中本敦浩
    • Organizer
      第22回位相幾何学的グラフ理論研究集会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2010-11-12
  • [Presentation] Hamiltonian cycles in bipartite toroidal graphs with partite set of degree four vertices2010

    • Author(s)
      A. Nakamoto
    • Organizer
      The 6th Cracow Conference
    • Place of Presentation
      Zgorzelisko, Poland
    • Year and Date
      2010-09-16
  • [Presentation] Hamiltonian cycles in bipartite toroidal graphs with partite set of degree four vertices2010

    • Author(s)
      中本敦浩
    • Organizer
      離散数学とその応用研究集会
    • Place of Presentation
      高知大学
    • Year and Date
      2010-07-31
  • [Presentation] Book embedding of toroidal bipartite graphs2010

    • Author(s)
      A. Nakamoto
    • Organizer
      8th French Combinatorial Conference
    • Place of Presentation
      Orsay, France
    • Year and Date
      2010-07-01
  • [Presentation] Vertex-face curve for bipartite quadrangulations on the torus2010

    • Author(s)
      A. Nakamoto
    • Organizer
      SIAM Conference on Discrete Mathematics
    • Place of Presentation
      Austin, Texas, USA
    • Year and Date
      2010-06-16
  • [Presentation] 2-Orientations of bipartite quadrangulations on the torus2010

    • Author(s)
      中本敦浩
    • Organizer
      岡村治子先生退職記念研究集会
    • Place of Presentation
      甲南大学
    • Year and Date
      2010-03-07
  • [Presentation] Book embedding of toroidal bipartite graphs2009

    • Author(s)
      中本敦浩
    • Organizer
      2009年応用数学合同研究集会
    • Place of Presentation
      龍谷大学
    • Year and Date
      2009-12-19
  • [Presentation] Hamiltonian cycles in bipartite quadrangulations on the torus2009

    • Author(s)
      A. Nakamoto
    • Organizer
      33rd Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      Newcastle, Australia
    • Year and Date
      2009-12-10
  • [Presentation] Book embedding of toroidal bipartite graphs2009

    • Author(s)
      中本敦浩
    • Organizer
      第21回位相幾何学的グラフ理論研究集会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2009-11-27
  • [Presentation] Hamiltonian cycles in bipartite quad-rangulations on the torus2009

    • Author(s)
      中本敦浩
    • Organizer
      離散数学とその応用研究集会
    • Place of Presentation
      茨城大学工学部
    • Year and Date
      2009-08-08
  • [Presentation] N-Flips in even triangulations and Dehn twists on the torus2009

    • Author(s)
      A. Nakamoto
    • Organizer
      British Combinatorial Conference
    • Place of Presentation
      University of St Andrews, United Kingdom
    • Year and Date
      2009-07-09
  • [Remarks]

    • URL

      http://www.ms.edhs.ynu.ac.jp/Nakamoto-lab/

URL: 

Published: 2013-07-31  

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