• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Book embedding of graphs on surfaces based on cycle finding problems

Research Project

Project/Area Number 15K04975
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionYokohama National University

Principal Investigator

Nakamoto Atsuhiro  横浜国立大学, 大学院環境情報研究院, 教授 (20314445)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsグラフ / 曲面 / 本型埋め込み / ページ数 / 種数 / ハミルトン閉路 / 平面グラフ / 射影平面グラフ / グラフの連結度
Outline of Final Research Achievements

For a given graph, determining the page number seems to be a very important problem in both theoretical and practical reasons. In this research, our goal is to describe a relation between genus and page number of graphs, and we have succeeded in giving an upper bound for the page number of a graph embeddable on a surface, finding a suitable cycle of a graph with a good property. In particular, we have been able to give an upper bound for the page number of locally planar graphs on any orientable surfaces, and that for projective-planar graphs with respect to their connectivity.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (25 results)

All 2017 2016 2015 Other

All Int'l Joint Research (1 results) Journal Article (14 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 14 results,  Open Access: 4 results,  Acknowledgement Compliant: 2 results) Presentation (10 results) (of which Int'l Joint Research: 7 results,  Invited: 1 results)

  • [Int'l Joint Research] (University of the Witwatersrand(南アフリカ)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Coloring of locally planar graphs on surfaces with one color class small2017

    • Author(s)
      A. Nakamoto and K. Ozeki
    • Journal Title

      Australasian J. Comb.

      Volume: 67 Pages: 101-108

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Note On 6-regular Graphs on the Klein Bottle2017

    • Author(s)
      M. Kasai, N. Matsumoto, A. Nakamoto, T. Nozawa, Y. Takiguchi, H. Seno
    • Journal Title

      Theory and Applications of Graphs

      Volume: 4

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] N-flips in even triangulations on the projective plane preserving chromatic number2017

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

      Yokohama Math. J.

      Volume: 63 Pages: 75-89

    • NAID

      120006459868

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quadrangulations on the projective plane with a K3,4-minor2017

    • Author(s)
      N. Matsumoto, A. Nakamoto and S. Yonekura
    • Journal Title

      Yokohama Math. J.

      Volume: 63 Pages: 117-129

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Cyclic 4-colorings of graphs on surfaces2016

    • Author(s)
      Atsuhiro Nakamoto, Kenta Noguchi, and Kenta Ozeki
    • Journal Title

      J. Graph Theory

      Volume: 82 Issue: 3 Pages: 265-278

    • DOI

      10.1002/jgt.21900

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Minor relation for quadrangulations on the projective plane2016

    • Author(s)
      N. Matsumoto, A. Nakamoto, S. Yonekura
    • Journal Title

      Discrete Appl. Math.

      Volume: 209 Pages: 296-302

    • DOI

      10.1016/j.dam.2015.07.037

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Odd complete minors in even embeddings on surfaces2016

    • Author(s)
      G. Fijavz, A. Nakamoto
    • Journal Title

      Discrete Math.

      Volume: 339 Issue: 1 Pages: 165-178

    • DOI

      10.1016/j.disc.2015.07.015

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Book embedding of locally planar graphs on orientable surfaces2016

    • Author(s)
      A. Nakamoto, T. Nozawa
    • Journal Title

      Discrete Math.

      Volume: 339 Issue: 11 Pages: 2672-2679

    • DOI

      10.1016/j.disc.2016.05.006

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Grunbaum colorings of triangulations on the projective plane2016

    • Author(s)
      M. Kasai, N. Matsumoto, A. Nakamoto
    • Journal Title

      Discrete Appl. Math.

      Volume: 215 Pages: 155-163

    • DOI

      10.1016/j.dam.2016.07.012

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Looseness and independence number of triangulations on closed surfaces2016

    • Author(s)
      A. Nakamoto, S. Negami, K. Ohba, Y. Suzuki
    • Journal Title

      Discuss. Math. Graph Theory

      Volume: 36 Issue: 3 Pages: 545-554

    • DOI

      10.7151/dmgt.1870

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generating 4-connected even triangulations on the sphere2015

    • Author(s)
      Naoki Matsumoto and Atsuhiro Nakamoto
    • Journal Title

      Discrete Mathematics

      Volume: 338 Issue: 1 Pages: 64-70

    • DOI

      10.1016/j.disc.2014.08.017

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Minor relations for quadrangulations on the sphere2015

    • Author(s)
      Sheng Bau, Naoki Matsumoto, Atsuhiro Nakamoto and Lijuan Zheng
    • Journal Title

      Graphs and Combinatotics

      Volume: 未定 Issue: 6 Pages: 2029-2036

    • DOI

      10.1007/s00373-014-1489-y

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] N-flips in 4-connected even triangulations on the sphere2015

    • Author(s)
      Y. Kawasaki, N. Matsumoto
    • Journal Title

      Graphs and Combinatorics

      Volume: 31 Issue: 6 Pages: 1889-1904

    • DOI

      10.1007/s00373-015-1574-x

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Extension to even triangulations on surfaces2015

    • Author(s)
      A. Nakamoto, K. Noguchi and K. Ozek
    • Journal Title

      SIAM Journal on iIscrete Mathematics

      Volume: 29 Issue: 4 Pages: 2075-2087

    • DOI

      10.1137/140963340

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] 偶多角形のひし形分解と射影平面の四角形分割2017

    • Author(s)
      中本敦浩
    • Organizer
      研究集会「直観幾何」
    • Place of Presentation
      熊本大学
    • Year and Date
      2017-02-11
    • Related Report
      2016 Research-status Report
  • [Presentation] Rhombus tilings of an even-sided polygon and projective quadrangulations2017

    • Author(s)
      Atsuhiro Nakamoto
    • Organizer
      The Second Malta Conference in Graph Theory and Combinatorics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Rhombus tilings of an even-sided polygon and projective quadrangulations2017

    • Author(s)
      Atsuhiro Nakamoto
    • Organizer
      5th International Combinatorics Conference
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 偶多角形のひし形分解と射影平面の四角形分割2017

    • Author(s)
      中本敦浩
    • Organizer
      応用数学合同研究集会
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Minor relation for quadrangulations on surfaces2016

    • Author(s)
      A. Nakamoto
    • Organizer
      ACCOTA 2016
    • Place of Presentation
      Los Cabos, Baja California, Mexico
    • Year and Date
      2016-11-28
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] 偶多角形のひし形分解と射影平面の四角形分割2016

    • Author(s)
      中本敦浩
    • Organizer
      第27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
      2016-11-11
    • Related Report
      2016 Research-status Report
  • [Presentation] Y-Rotations in quadrangulations on the projective plane and rhombus tilling of a polygon2016

    • Author(s)
      中本敦浩
    • Organizer
      NAO-Asia 2016
    • Place of Presentation
      新潟大学
    • Year and Date
      2016-08-01
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] 3-正則2部グラフのSplitter theoremに向けて2015

    • Author(s)
      中本敦浩
    • Organizer
      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
      2015-11-13
    • Related Report
      2015 Research-status Report
  • [Presentation] Reductions of even triangulations on surfaces2015

    • Author(s)
      A. Nakamoto
    • Organizer
      the 9th KIAS Combinatorics Workshop
    • Place of Presentation
      Bloomvista in Yangpyeong (Seoul)
    • Year and Date
      2015-09-11
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Diagonal flips in plane graphs with triangular and quadrangular faces2015

    • Author(s)
      A. Nakamoto
    • Organizer
      The 8th Slovenian Conference
    • Place of Presentation
      Kranjska Gora, Slovenia
    • Year and Date
      2015-06-21
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research

URL: 

Published: 2015-04-16   Modified: 2022-02-22  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi