2015 Fiscal Year Final Research Report
A study on invariants that guarantee the existence of cycles and trees
| Project/Area Number |
24740074
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kinki University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | ハミルトン閉路 / 次数和条件 / 全域木 |
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| Outline of Final Research Achievements |
In 2008, Ozeki and I discovered a rule of a degree sum condition with the order, the connectivity and the independence number of a graph for the existence of a hamiltonian cycle. The rule is that the lower bound on the degree condition is an arithmetic progression with common difference of ``the independence number - 1''.
We proved that the rule holds for degree sum condition of two, three or four vertices, and conjectured the rule holds for degree sum condition of at least five vertices. Moreover, we posed a similar conjecture for the circumference. For these two conjectures, we settled the conjecture on hamiltonicity, and the conjecture on circumference for a degree sum condition of four vertices.
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| Free Research Field |
グラフ理論
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