Standard methods for the study of forbidden subgraphs

• Project/Area Number: 25330017
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Nihon 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: ¥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.

Research Products

• [Int'l Joint Research] Georgia Southern University/Georgia State University/Vanderbilt University(米国)
• [Int'l Joint Research] Technical University of Freiberg(ドイツ)
• [Int'l Joint Research] University of Twente(オランダ)
• [Int'l Joint Research] TU Bergakademie Freiberg(ドイツ)
• [Int'l Joint Research] Georgia State Univerity/Vanderbilt University(米国)
• [Journal Article] Spanning trees homeomorphic to a small tree (2016)
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The Ryjacek closure and a forbidden subgraph (2016)
  • 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
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Extendability of the complementary prism of bipartite graphs (2016)
  • Author(s): Nawarat Ananchuen, Watcharaphong Ananchuen and Akira Saito
  • Journal Title: Australasian Journal of Combinatorics Volume: 66 Pages: 436-448
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Forbidden triples generating a finite set of 3-connected graphs (2015)
  • Author(s): Yoshimi Egawa, Jun Fujisawa, Michitaka Furuya, Akira Saito and Michael D. Plummer
  • Journal Title: Electronic Journal of Combinatorics Volume: 22
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Perfect matchings avoiding prescribed edges in a star-free graph (2015)
  • 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
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A note on graphs contraction-critical with respect to independence number (2014)
  • 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
  • Peer Reviewed
• [Journal Article] Forbidden subgraphs generating a finite set (2013)
  • 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
  • Peer Reviewed
• [Journal Article] The existence of a 2-factor in a graph satisfying the local Chvatal-Erdos condition (2013)
  • 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
  • Peer Reviewed
• [Presentation] Forbidden subgraphs in edge-colored graphs (2017)
  • Author(s): Akira Saito
  • Organizer: 2017 Joint Mathematics Meetings
  • Place of Presentation: Hyatt Regency Atlanta, Atlanta, USA
  • Year and Date: 2017-01-06
  • Int'l Joint Research / Invited
• [Presentation] Toughness, binding number and restricted matching extension (2016)
  • 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
• [Presentation] The Chvatal-Erdos condition and a 2-factor with two components (2016)
  • 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
• [Presentation] Forbidden subgraphs and 2-factors in graphs (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Forbidden subgraphs and matchings in graphs (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Precoloring extension involving pairs of vertices of small distance (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Precoloring extension involving pairs of vertices of small distance (2015)
  • Author(s): Akira Saito
  • Organizer: Freiberger Graphentheorietage
  • Place of Presentation: TU Bergakademie Freiberg, Freiberg(Germany)
  • Year and Date: 2015-12-03
  • Int'l Joint Research / Invited
• [Presentation] Forbidden subgraphs and 2-factors (2015)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Extendability of the complementary prism of a bipartite graph (2015)
  • 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
• [Presentation] Spanning trees homeomorphic to a small tree (2015)
  • 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
  • Int'l Joint Research
• [Presentation] The Ryjacek closure and a forbidden subgraph (2015)
  • 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
• [Presentation] Spanning trees homeomorphic to a small tree (2014)
  • 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
• [Presentation] Precoloring extension involving pairs of vertices of small distance (2014)
  • 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
  • Invited
• [Presentation] A spanning tree homeomorphic to a small tree (2014)
  • 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
  • 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
• [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
• [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