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

2010 Fiscal Year Final Research Report

• 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
• Keywords: 組合せ論 / グラフ理論

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
• [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] 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
• [Remarks] ホームページ等
  • URL: http://www.nat.gunma-ct.ac.jp/Souran/shizen/fujita.htm