2013 Fiscal Year Final Research Report
structural graph theory and eifficient algorithm for graph coloring problems
| Project/Area Number |
21684002
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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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 | National Institute of Informatics |
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Principal Investigator |
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| Project Period (FY) |
2009-04-01 – 2013-03-31
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| Keywords | グラフ彩色 / アルゴリズム |
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| Research Abstract |
In this research, we have worked on graph coloring problem for
1. graphs on a surface, and 2. minor-closed family of graphs.
Concerning the first one, we give several algorithmic results. Namely. we give a polynomial time algorithm for deciding 5-list-colorability of graphs on a fixed surface, and for deciding 3-list-colorablity of graphs of girth five on a fixed surface. Concerning the second one, we show that minimal-counterexample to the famous Hadwiger's conjecture is 0.2k-connected for the case k. This is the first step toward a chacterization of such a minimal-counterexample.
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