Research on graphs densely embedded on a closed surface

2012 Fiscal Year Final Research Report

• Project/Area Number: 23654041
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Keio University
• Principal Investigator: OTA Katsuhiro 慶應義塾大学, 理工学部, 教授 (40213722)
• Co-Investigator(Kenkyū-buntansha): ODA Yoshiaki 慶應義塾大学, 理工学部, 准教授 (90325043)
• Project Period (FY): 2011 – 2012
• Keywords: グラフ理論 / 三角形分割 / 閉曲面 / 染色数 / Hadwiger予想 / データベース

Research Abstract

We made a program generating all irreducible triangulations of a surface by applying vertex-splittings from a bouquet, one consisting of only one vertex. The list we obtained for the torus, it coincides with the list previously known. We also enumerate al

Research Products

• [Journal Article] Hamiltonian cycles with all small even chords (2012)
  • Author(s): G. Chen, K. Ota, A. Saito and Y. Zhao
  • Journal Title: Discrete Math Volume: 312 Pages: 1226-1240
  • Peer Reviewed
• [Presentation] Clique minors, chromatic numbers for degree sequences in graphs (2013)
  • Author(s): 太田克弘
  • Organizer: 日本数学会2013年度年会
  • Place of Presentation: 京都大学
  • Year and Date: 2013-03-20
• [Presentation] Clique minors chromatic numbers for degree sequences (2013)
  • Author(s): 太田克弘
  • Organizer: Hakata Workshop 2013 -Combinatorics and its applications-
  • Place of Presentation: 九州大学(リファレンスビル博多駅東ビル)
  • Year and Date: 2013-01-26
• [Presentation] Hajos number and chromatic number for near regular degree sequences (2012)
  • Author(s): 挾間龍
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2012-12-20
• [Remarks] 頂点数,次数列・染色数毎のグラフの個数について,下記で公開している.
  • URL: http://www.math.keio.ac.jp/~ohta/graphenum.html