A STUDY ON PARTITION PROBLEMS IN HIGHLY CONNECTED GRAPHS AND FORBIDDEN SUBGRAPHS

• Project/Area Number: 20740068
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Gunma National College of Technology
• Principal Investigator: FUJITA Shinya Gunma National College of Technology, 一般教科, 講師 (60424206)
• Project Period (FY): 2009 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 組合せ論 / グラフ理論 / グラフの連結度 / 非分離部分グラフ / グラフの頂点分割 / グラフの連続度 / 禁止部分グラフ / 点素な部分グラフ

Research Abstract

In this research, I focused on the Thomassen's conjecture concerning a partition problem in graph connectivity. I worked on this problem in view of the study on forbidden subgraphs and tried to get some partial results. As a result, I could obtain many nice results in this area.

Research Products

• [Journal Article] Contractible small subgraphs in highly connected graphs (2010)
  • Author(s): 藤田慎也、河原林健一
  • Journal Title: Graphs and Combinatorics 26巻 Pages: 499-511
  • Peer Reviewed
• [Journal Article] Non-separating even cycles in highly connected graphs (2010)
  • Author(s): 藤田慎也、河原林健一
  • Journal Title: Combinatorica 30巻 Pages: 565-580
  • Peer Reviewed
• [Journal Article] The balanced decomposition number and vertex connectivity (2010)
  • Author(s): 藤田慎也、Henry Liu
  • Journal Title: SIAM Journal on Discrete Mathematics 24巻 Pages: 1597-1616
  • Peer Reviewed
• [Journal Article] Non-separating even cycles in highly connected graphs (2010)
  • Author(s): 藤田慎也、河原林健一
  • Journal Title: Combinatorica Volume: 30 Pages: 565-580
  • Peer Reviewed
• [Journal Article] The balanced decomposition number and vertex connectivity (2010)
  • Author(s): 藤田慎也、Henry Liu
  • Journal Title: SIAM Journal on Discrete Mathematics Volume: 24 Pages: 1597-1616
  • Peer Reviewed
• [Journal Article] Contractible small subgraphs in highly connected graphs (2010)
  • Author(s): 藤田慎也、河原林健一
  • Journal Title: Graphs and Combinatorics Volume: 26 Pages: 499-511
  • Peer Reviewed
• [Journal Article] On a sharp degree sum condition for disjoint chorded cycles in graphs (2010)
  • Author(s): 千葉周也、藤田慎也、Yunshu Gao、Guojun Li
  • Journal Title: Graphs and Combinatorics 26 Pages: 173-186
  • Peer Reviewed
• [Journal Article] A rainbow k-matching in the complete graph with r colors (2009)
  • Author(s): 藤田慎也、金子篤司、鈴木一弘 Ingo Schiermeyer
  • Journal Title: The Electronic Journal of Combinatorics 16(-(オシライン))
  • Peer Reviewed
• [Journal Article] Degree conditions for the partition of a graph into cycles, edges and isolated vertices (2009)
  • Author(s): 藤田慎也
  • Journal Title: Discrete Mathematics 309 Pages: 3534-3540
  • Peer Reviewed
• [Journal Article] Note on non-separating and removable cycles in highly connected graphs (2009)
  • Author(s): 藤田慎也、河原林健元
  • Journal Title: Discrete Applied Mathematics 157 Pages: 398-399
  • Peer Reviewed
• [Journal Article] Balanced decomposition of a vertex-colored graph (2008)
  • Author(s): 藤田慎也、中上川友樹
  • Journal Title: Discrete Applied Mathematics 156 Pages: 3339-3344
  • Peer Reviewed
• [Journal Article] K1, 3-factors in graphs (2008)
  • Author(s): 江川嘉美、藤田慎也、太田克弘
  • Journal Title: Discrete Mathematics 308 Pages: 5965-5973
  • Peer Reviewed
• [Presentation] グラフのedge-coloringに関する最近の話題 (2010)
  • Author(s): 藤田慎也
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学(特別講演)
  • Year and Date: 2010-09-22
• [Presentation] Proper connection in graphs (2010)
  • Author(s): 藤田慎也
  • Organizer: 日本数学会年会
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2010-03-25
• [Presentation] Contractible small subgraphs in highly connected graphs (2009)
  • Author(s): 藤田慎也
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24
• [Presentation] Non-separating even cycles in highly connected graphs (2008)
  • Author(s): 藤田慎也
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-25
• [Book] ITText離散数学 (2010)
  • Author(s): 藤田慎也, 他
  • Total Pages: 256
  • Publisher: オーム社
• [Book] I Tテキスト 離散数学 (2010)
  • Author(s): 松原良太、大島彰昇、藤田慎也、小関健太、中上川友樹、佐久間雅、津垣正男
  • Total Pages: 256
  • Publisher: オーム社
• [Remarks] ホームページ等
  • URL: http://www.nat.gunma-ct.ac.jp/Souran/shizen/fujita.htm