2011 Fiscal Year Final Research Report
Research on graphs characterized by forbidden minors
| Project/Area Number |
20340023
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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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) |
TAMURA Akihisa 慶應義塾大学, 理工学部, 教授 (50217189)
ODA Yoshiaki 慶應義塾大学, 理工学部, 准教授 (90325043)
ISHII Ippei 慶應義塾大学, 理工学部, 准教授 (90051929)
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| Co-Investigator(Renkei-kenkyūsha) |
NAKAMOTO Atsuhiro 横浜国立大学, 教育人間科学部, 准教授 (20314445)
YAMASHITA Tomoki 近畿大学, 理工学部, 講師 (10410458)
FUJISAWA Jun 慶應義塾大学, 商学部, 専任講師 (00516099)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 組合せ論 |
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| Research Abstract |
From a given graph G, a graph obtained from a subgraph of G by contracting several edges is called a minor of G. Some important classes of graphs, such as planar graphs are closed under the operation taking a minor, and are characterized by forbidden minors. In this research, we extend some results of planar graphs concerning cycles, spanning trees and factors, from the point of view of forbidden minors. In particular, we obtained some results on the toughness and the spanning trees in graphs without complete bipartite minors. We also considered similar problems on the forbidden induced subgraphs.
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