| Project/Area Number |
14540137
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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) |
MATSUMOTO Satoshi Tokai University, School of Science, Assistant Professor, 理学部, 講師 (30307235)
MATSUI Yasuko Tokai University, School of Science, Assistant Professor, 理学部, 講師 (10264582)
HARA Masao Tokai University, School of Science, Associate Professor, 理学部, 助教授 (10238165)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 2003: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2002: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Keywords | graph theory / poset / upper bound graph / double bound graph / semi bound graph |
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| Research Abstract |
We consider upper bound graphs, double bound graphs and semi bound graphs in terms of non-maximal clique covers, intervals and order ideals. Using these properties, we obtain some characterization of double bound graphs and semi bound graphs.
Based on properties of non-maximal cliques, we deal with some properties of upper bound graphs and double bound graphs on infinite posets. We consider properties on upper bound graphs and double bound graphs of infinite tree posets and obtain characterizations of these graphs.
Using concepts of hereditariness of bound graphs, we obtain some properties on some kinds of hereditary bound graphs. By these results, we obtain characterizations of hereditary upper bound graphs, hereditary double bound graphs and hereditary semi bound graphs in terms of forbidden subgraphs and subposets. We also consider some properties on subposets corresponding forbidden subgraphs.
We deal with properties on maximal posets and minimal posets of a poset family with same upper bound graph. We also consider transformations between posets whose upper bound graphs are the same. We obtain that two posets with the same canonical poset and the same upper bound graph can be transformed into each other by a finite sequence of two transformations, that is, x<y-additions and x<y-deletions.
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