| Project/Area Number |
14540134
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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 | HIROSHIMA UNIVERSITY (2003-2004)
Keio University (2002) |
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Principal Investigator |
ENOMOTO Hikoe Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00011669)
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| Co-Investigator(Kenkyū-buntansha) |
OTA Katsuhiro Keio University, Faculty of Science and Technology, Professor, 理工学部, 教授 (40213722)
MATSUMOTO Makoto Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70231602)
江端 満彦 広島大学, 大学院・理学研究科, 助手 (70363041)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | graph / cycle / factor / decree condition / independence number / connectivity / 次数条件 / 因子分解 / (g, f)-因子 / 分割 / 孤立点 / 成分因子 / 彩色数 / リスト彩色数 / 直径 |
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| Research Abstract |
(1)In 1997, Brandt and others proved that a graph G of order at least 4k and the degree sum of nonadjacent vertices at least |V(G)| can be partitioned into k disjoint cycles. This result is generalized in several ways. We weakened the degree sum assumption to |V(G)|-k+1 by allowing degenerated cycles (edges and isolated vertices). We also obtained sufficient conditions on the minimum degree to assure that each cycle passes through a specified vertex. We also solved the problem in which each cycle passes through a specified vertex or a specified edge. Furthermore, we solved the problem for bipartite graphs.
(2)Erdos-Chvatal theorem says that if the independence number is not larger than the connectivity, the graph contains a Hamiltonian cycle. We generalized this result to the existence of a long cycle.
(3)We investigated the maximum order of a graph without k disjoint cycles and the independence number is at most α.
(4)We proved that if G is an (mg+m-1,mf-m+1)-graph and if k≦g(x)≦f(x) for any vertex x of G,G can be factorized into (g,f)-factors in which each factor contains k specified edges.
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