| Project/Area Number |
18540139
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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 (00188583)
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| Co-Investigator(Kenkyū-buntansha) |
HARA Masao Tokai University, School of Science, Associate Professor (10238165)
MATSUI Yasuko Tokai University, School of Science, Associate Professor (10264582)
MATSUMOTO Satoshi Tokai University, School of Science, Associate Professor (30307235)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,850,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥450,000)
Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2006: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | graph theory / poset / upper bound graph / double bound graph / forbidden subgraph / forbidden subposet / semi bound graphs / upper bound grap / k-tree / semi bound graph |
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| Research Abstract |
We consider upper bound graphs and double bound graphs in terms of induced subgraphs and subposets. We also deal with the relations between induced subgraphs and subposets of bound graphs in terms of clique covers.
Based on properties of clique covers of double bound graphs, we deal with properties on maximal posets and minimal posets of a poset family with same semi bound graph. We obtain of the diameter and the radius of the family of posets with same semi bound graph.
We also consider k-trees in terms of leafages. We show that there exists a k-tree for a given number of leafages.
We deal with properties on principal order ideals and intervals. Using these properties, we consider families of cliques on forbidden subgraphs. We obtain characterizations of some kinds of subfamily of upper bound graphs in terms of forbidden upper bound subgraphs. For example, star n-gons are forbidden upper bound subgraphs of upper bound chordal graphs. 2K_2 is a forbidden upper bound subgraphs of upper bound split graphs. For a graph G, G and its complement are Meyniel graphs if and only if G does not contain C_5 , P_5 and the house graph as induced subgraphs.
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