2013 Fiscal Year Final Research Report
Generation of regular graphs and its applications
| Project/Area Number |
22740068
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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 | Keio University (2011-2013)
Kochi University (2010) |
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Principal Investigator |
FUJISAWA Jun 慶應義塾大学, 商学部, 准教授 (00516099)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | グラフ / 位相幾何学的グラフ理論 / 閉路問題 / 因子問題 / マッチング |
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| Research Abstract |
The following is the main part of the results obtained in this research. First a conjeture posed by Grunbaum and Nash-Williams turned out to be true if the toughness of the graph is 1. Next, on the triangulations of the plane, projective plane, torus and Klein bottle, many results concerning the problem "what kind of a matching is extendable to a perfect matching" are proved. In addition to the above, many results are obtained, as the proof of Lai et al.'s conjecture, a generalization of Jackson's theorem, and so on.
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