2015 Fiscal Year Final Research Report
{a,b}-factors of regular graphs
| Project/Area Number |
25400187
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Ibaraki University |
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Principal Investigator |
Kano Mikio 茨城大学, 理工学研究科, 名誉教授 (20099823)
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| Research Collaborator |
TSUGAKI Masao
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | 離散数学 / グラフ理論 / グラフの因子 / 正則グラフ / 全域木 |
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| Outline of Final Research Achievements |
Let a, b and r be positive integers such that a+b=r and a≦r/2. We want to prove the following conjecture: If r is odd, then every r-regular graph has an {a,b}-factor. We showed that if either a is even or a is odd and r/3≦a≦r/2, then the conjecture holds. On the other, it was recently shown that the conjecture does not hold if (a+1)(a+2)≦r. However there are unsolved cases. We also obtained some results on factors of graphs and spanning trees of graph, which are related to the above conjecture.
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| Free Research Field |
離散数学
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