New colored graphs towards a Brualdi-Hollingsworth conjecture
| Project/Area Number |
21740085
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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 | Kanagawa University |
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Principal Investigator |
SUZUKI Kazuhiro Kanagawa University, 工学部, 助手 (50514410)
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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 |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2009: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Keywords | 離散数学 / グラフ理論 / 全域木 / 辺彩色 / 辺着色 / 異色全域木 / f-異色グラフ / f-chromatic / BH予想 / グラフ / graph |
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| Research Abstract |
Brualdi et al. conjectured that a properly edge-colored complete graph of order 2n(>5)with 2n-1 colors can be decomposed into n edge-disjoint heterochromatic spanning trees. We generalized this conjecture by defining an f-chromatic graph, by which we can study stepwise the conjecture. In particular, we proved the generalized conjecture with f(c)=n-2. Moreover, we proved a necessary and sufficient condition for existence of an f-chromatic spanning forest with exactly w components, and generalized two previous results by applying the condition.
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Report
(3 results)
Research Products
(10 results)
