| Project/Area Number |
24340021
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Keio University |
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Principal Investigator |
Ota Katsuhiro 慶應義塾大学, 理工学部, 教授 (40213722)
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| 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)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMASHITA Tomoki 近畿大学, 理工学部, 准教授 (10410458)
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| 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
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥9,880,000 (Direct Cost: ¥7,600,000、Indirect Cost: ¥2,280,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2012: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
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| 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 / グラフマイナー / 彩色問題 / 森グラフ / 国際情報交換 / アメリカ / 完全マッチング / 台湾 / タフネス / 国際研究者交流 / アメリカ:台湾 |
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| 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.
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