2005 Fiscal Year Final Research Report Summary
On bound graphs and simplicial vertices
| 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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| Keywords | graph theory / poset / upper bound graph / double bound graph / semi bound graph / forbidden subposet / forbidden subgraph |
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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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Research Products
(20 results)
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[Book] 離散数学2004
Author(s)
土屋守正 他
Total Pages
217
Publisher
横浜図書
Description
「研究成果報告書概要(和文)」より
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