2013 Fiscal Year Final Research Report
On Thomassen's conjecture and 2-factors of claw-free graphs
| Project/Area Number |
22540152
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Nihon University |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | グラフ理論 / ハミルトンサイクル / Thomassen予想 / ２因子 / ライングラフ |
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| Research Abstract |
First, we studied the upper bounds of the number of components of 2-factors of low-connected line graphs, which are given by using the maximum independence number. And we got the following result: a 3-connected claw-free graph has a 2-factor in which the number of components is at most 2a/5, where a is the maximum independence number. Next we considered cubic graphs, which is very important family of graphs for Thomassen's conjecture and many important problems and conjectures in Graph theory. And we showed that if Bondy's conjecture on cubic graphs holds, then Thomassen's conjecture holds for the case of the minimum degree at least five.
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