2010 Fiscal Year Final Research Report
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 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Kanagawa University |
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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Keywords | 離散数学 / グラフ理論 |
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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