Integrated research of extremal problems on graph factors, minors and subgraphs

2016 Fiscal Year Final Research Report

• Project/Area Number: 24340021
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• 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): 藤沢 潤 慶應義塾大学, 商学部, 准教授 (00516099) ; 田村 明久 慶應義塾大学, 理工学部, 教授 (50217189) ; 石井 一平 慶應義塾大学, 理工学部, 非常勤講師 (90051929) ; 小田 芳彰 慶應義塾大学, 理工学部, 准教授 (90325043)
• Co-Investigator(Renkei-kenkyūsha): YAMASHITA Tomoki 近畿大学, 理工学部, 准教授 (10410458)
• Research Collaborator: ENOMOTO Hikoe 元広島大学, 大学院, 教授 ; OZEKI Kenta 国立情報学研究所, 特任助教 ; TSUCHIYA Shoichi 専修大学, 講師 ; NOGUCHI Kenta 東京電機大学, 助教 ; SAKUMA Tadashi 山形大学, 准教授
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: グラフ理論 / 極値問題 / 弦付きサイクル / シータグラフ / マッチング拡張性 / Hadwiger予想 / 禁止部分グラフ

Outline of Final Research Achievements

The problems in extremal graph theory is to find the minimum number of edges or a sharp minimum degree condition for a graph G to contain a prescribed subgraph H. In this research, by considering the problems from the unified point of view of factor problems, graph minor problems, and subgraph finding problems, we shall go into a new area of extremal graph theory. In particular, we focus on extremal problems of forests, vertex-disjoint chorded cycles and theta subgraphs, matching extendability, etc. Also, related to Hadwiger's conjecture, one of the most famous conjectures in graph theory, we propose the notion of rho-coloring, and give an alternative and much simpler proof of Hadwiger's conjecture for degree sequences.

Free Research Field

離散数学