| Project/Area Number |
21740081
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kitasato University |
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Principal Investigator |
YAMASHITA Tomoki Kitasato University, 一般教育部, 講師 (10410458)
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| Project Period (FY) |
2009 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 組合せ論 / グラフ理論 / ハミルトン閉路 / 次数和条件 / ハミルトン路 |
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| Research Abstract |
We researched the concept of relative length which is a generalization of a hamiltonian cycle, and obtained a condition of the degree sum of four vertices for relative length of a graph to be at most 1. By this result, we gave a new evidence for our conjecture concerning degree sum conditions for the existence of cycles. Moreover, we studied about the circumference version of this conjecture, and settled a part of it. On the other hand, we investigated degree sum conditions for hamiltonain cycles, cycles passing through specified vertices and the circumference in bipartite graphs. We could see the analogue for degree sum conditions in general graphs, but we could not see that for the degree sum conditions in bipartite graphs.
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