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Standard methods for the study of forbidden subgraphs

Research Project

Project/Area Number 25330017
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Theory of informatics
Research InstitutionNihon University

Principal Investigator

SAITO Akira  日本大学, 文理学部, 教授 (90186924)

Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords禁止部分グラフ / グラフ / ハミルトンサイクル / 因子 / グラフ理論 / マッチング / スター / 連結度 / 頂点彩色 / 縮約 / 離散数学 / 組合せ論
Outline of Final Research Achievements

For a set F of finite connected graphs, a graph G is said to be F-free if G does not contain an induced subgraph which is isomorphic to any member of F. The set F is often referred as forbidden subgraphs. In this research, we have constructed infinite sequences of graphs consisting of graphs with relatively high symmetry, and studied induced subgraphs commonly contained in each member of the sequences. This has led us to establish a common methods which are applicable to a number of studies on forbidden subgraphs. Then we have applied these methods and solved several problems concerning forbidden subgraphs and demonstrated the effectiveness of these methods.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (31 results)

All 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (5 results) Journal Article (9 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 9 results,  Acknowledgement Compliant: 5 results,  Open Access: 1 results) Presentation (17 results) (of which Int'l Joint Research: 7 results,  Invited: 8 results)

  • [Int'l Joint Research] Georgia Southern University/Georgia State University/Vanderbilt University(米国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Technical University of Freiberg(ドイツ)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] University of Twente(オランダ)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] TU Bergakademie Freiberg(ドイツ)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Georgia State Univerity/Vanderbilt University(米国)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Spanning trees homeomorphic to a small tree2016

    • Author(s)
      Akira Saito and Kazuki Sano
    • Journal Title

      Discrete Mathematics

      Volume: 338 Issue: 2 Pages: 2260-2274

    • DOI

      10.1016/j.disc.2015.10.004

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The Ryjacek closure and a forbidden subgraph2016

    • Author(s)
      Akira Saito and Liming Xiong
    • Journal Title

      Dicsussiones Mathematicae Graph Theory

      Volume: 36 Issue: 3 Pages: 621-681

    • DOI

      10.7151/dmgt.1876

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Extendability of the complementary prism of bipartite graphs2016

    • Author(s)
      Nawarat Ananchuen, Watcharaphong Ananchuen and Akira Saito
    • Journal Title

      Australasian Journal of Combinatorics

      Volume: 66 Pages: 436-448

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Forbidden triples generating a finite set of 3-connected graphs2015

    • Author(s)
      Yoshimi Egawa, Jun Fujisawa, Michitaka Furuya, Akira Saito and Michael D. Plummer
    • Journal Title

      Electronic Journal of Combinatorics

      Volume: 22

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Perfect matchings avoiding prescribed edges in a star-free graph2015

    • Author(s)
      Yoshimi Egawa, Jun Fujisawa, Michael D. Plummer, Akira Saito and Tomoki Yamashita
    • Journal Title

      Discrete Mathematics

      Volume: 339 Issue: 12 Pages: 2260-2274

    • DOI

      10.1016/j.disc.2015.05.014

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Precoloring extension involving pairs of vertices of small distance,2014

    • Author(s)
      Chihoko Ojima, Akira Sato and Kazuki Sano
    • Journal Title

      Discrete Applied Mathematics

      Volume: 166 Pages: 170-177

    • DOI

      10.1016/j.dam.2013.10.012

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A note on graphs contraction-critical with respect to independence number2014

    • Author(s)
      Michael D. Plummer and Akira Saito
    • Journal Title

      Discrete Mathematics

      Volume: 325 Pages: 85-91

    • DOI

      10.1016/j.disc.2014.02.004

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Forbidden subgraphs generating a finite set2013

    • Author(s)
      J. Fujisawa, M. D. Plummer and A. Saito
    • Journal Title

      Discrete Mathematics

      Volume: 313 Issue: 19 Pages: 1835-1842

    • DOI

      10.1016/j.disc.2012.05.015

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The existence of a 2-factor in a graph satisfying the local Chvatal-Erdos condition2013

    • Author(s)
      Guantao Chen, Akira Saito and Songling Shan
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 27 Issue: 4 Pages: 1788-1799

    • DOI

      10.1137/12090037x

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Forbidden subgraphs in edge-colored graphs2017

    • Author(s)
      Akira Saito
    • Organizer
      2017 Joint Mathematics Meetings
    • Place of Presentation
      Hyatt Regency Atlanta, Atlanta, USA
    • Year and Date
      2017-01-06
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Toughness, binding number and restricted matching extension2016

    • Author(s)
      斎藤 明
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Year and Date
      2016-09-16
    • Related Report
      2016 Annual Research Report
  • [Presentation] The Chvatal-Erdos condition and a 2-factor with two components2016

    • Author(s)
      斎藤 明
    • Organizer
      日本数学会年会
    • Place of Presentation
      筑波大学(茨城県・つくば市)
    • Year and Date
      2016-03-17
    • Related Report
      2015 Research-status Report
  • [Presentation] Forbidden subgraphs and 2-factors in graphs2016

    • Author(s)
      Akira Saito
    • Organizer
      1117th Meeting of the American Mathematical Society
    • Place of Presentation
      University of Georgia, Athens, Georgia(U.S.A.)
    • Year and Date
      2016-03-02
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Forbidden subgraphs and matchings in graphs2016

    • Author(s)
      Akira Saito
    • Organizer
      Symposium on Graph Theory and Applications 2016
    • Place of Presentation
      Ateneo de Manila University, Manila(The Philippines)
    • Year and Date
      2016-01-15
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Precoloring extension involving pairs of vertices of small distance2016

    • Author(s)
      Akira Saito
    • Organizer
      Symposium on Graph Theory and Applications 2016
    • Place of Presentation
      Ateneo de Manila University, Manila(The Philippines)
    • Year and Date
      2016-01-13
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Precoloring extension involving pairs of vertices of small distance2015

    • Author(s)
      Akira Saito
    • Organizer
      Freiberger Graphentheorietage
    • Place of Presentation
      TU Bergakademie Freiberg, Freiberg(Germany)
    • Year and Date
      2015-12-03
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Forbidden subgraphs and 2-factors2015

    • Author(s)
      Akira Saito
    • Organizer
      The Second Japan-Sino Symposium on Graph Theory, Combinatorics and Their Applications
    • Place of Presentation
      東京理科大学(東京都・新宿区)
    • Year and Date
      2015-11-03
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Extendability of the complementary prism of a bipartite graph2015

    • Author(s)
      斎藤 明
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      京都産業大学(京都府・京都市)
    • Year and Date
      2015-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] Spanning trees homeomorphic to a small tree2015

    • Author(s)
      Akira Saito
    • Organizer
      International Conference on Graph Theory in Honor of Adrian Bondy's 70th Birthday
    • Place of Presentation
      福州大学、福州(中国)
    • Year and Date
      2015-04-18
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] The Ryjacek closure and a forbidden subgraph2015

    • Author(s)
      斎藤 明
    • Organizer
      日本数学会年会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-22
    • Related Report
      2014 Research-status Report
  • [Presentation] Spanning trees homeomorphic to a small tree2014

    • Author(s)
      斎藤 明
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25
    • Related Report
      2014 Research-status Report
  • [Presentation] Precoloring extension involving pairs of vertices of small distance2014

    • Author(s)
      Akira Saito
    • Organizer
      Japanese Conference on Combinatorics and its Applications 2014
    • Place of Presentation
      筑波大学
    • Year and Date
      2014-08-27
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] A spanning tree homeomorphic to a small tree2014

    • Author(s)
      Akira Saito
    • Organizer
      SIAM Conference on Discrete Mathematics
    • Place of Presentation
      Hyatt Regency Minneapolis, Minneapolis, Minnesota U.S.A.
    • Year and Date
      2014-06-18
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Precoloring extension involving pairs of vertices of small distance

    • Author(s)
      Akira Saito
    • Organizer
      24th. British Combinatorial Conference
    • Place of Presentation
      Royal Holloway, University of London, England
    • Related Report
      2013 Research-status Report
  • [Presentation] Precoloring extension involving pair of vertices of small distance

    • Author(s)
      斎藤 明、佐野和貴、尾島千穂子
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Contraction-critical graphs with respect to independence number

    • Author(s)
      斎藤 明、Michael D. Plummer
    • Organizer
      日本数学会年会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2022-01-24  

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