2009 Fiscal Year Final Research Report
A 2-Factor in a Graph and the Number of Its Components
| Project/Area Number |
19500017
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Nihon University |
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Principal Investigator |
SAITO Akira Nihon University, 文理学部, 教授 (90186924)
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| Project Period (FY) |
2007 – 2009
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| Keywords | グラフ / ハミルトンサイクル / 因子 / 成分 / 禁止部分グラフ / 最小次数 |
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| Research Abstract |
In this research, we interpreted a hamiltonian cycle as a 2-factor with one component, and investigated conditions which differentiate the existence of a hamiltonian cycle and that of a 2-factor, or more generally, which give information on the number of components in a 2-factor. We chose Dirac's condition, the Chvatal-Erdos condition and conditions based on forbidden subgraphs. We discovered that while neither Dirac's condition nor the Chvatal-Erdos condition gives any information on the number of components in a 2-factor, there is a notable difference between forbidden subgraphs forcing the existence of a hamiltonian cycle and those forcing the existence of a 2-factor.
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[Presentation] Bipartite Graphs(招待講演)2008
Author(s)
斎藤明
Organizer
The second International Conference on Mathematics and Natural Sciences
Place of Presentation
Bandung Institute of Technology, Bandung, Indonesia
Year and Date
2008-10-28
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