| Project/Area Number |
16540118
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokai University |
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Principal Investigator |
TSUCHIYA Morimasa Tokai University, School of Science, Professor, 理学部, 教授 (00188583)
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| Co-Investigator(Kenkyū-buntansha) |
HARA Masao Tokai University, School of Science, Associate Professor, 理学部, 助教授 (10238165)
MATSUI Yasuko Tokai University, School of Science, Assistant Professor, 理学部, 講師 (10264582)
MATSUMOTO Satoshi Tokai University, School of Science, Assistant Professor, 理学部, 講師 (30307235)
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| Project Period (FY) |
2004 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2005: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2004: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | graph theory / poset / upper bound graph / double bound graph / semi bound graph / forbidden subposet / forbidden subgraph / simplicial vertex / subposet |
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| Research Abstract |
We consider upper bound graphs, double bound graphs and semi bound graphs in terms of simplicial vertices and non-maximal clique covers. Using these properties, we obtain some characterization of semi bound graphs. We also deal with transformations between posets whose semi bound graphs are the same. We obtain that upper bound of distances between two posets with the same double canonical poset and the same semi bound graph. Based on properties of simplicial vertices, we obtain a construction method of upper bound graphs
We also consider upper bound graphs and double bound graphs in terms of forbidden subgraphs and forbidden subposets. We deal with some properties on subposets corresponding to subgraphs. We obtain some properties on m-subposets, (n,m)-subposets and induced subgraphs.
Using concepts of clique covers and simplicial vertices, we obtain some properties on triangle-free subgraphs. By these results, we obtain characterizations of split double bound graphs, threshold double bound graphs and difference bound graphs in terms of forbidden subgraphs and subposets.
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