2004 Fiscal Year Final Research Report Summary
Fundamental and application oriented studies of discrete structures
| Project/Area Number |
14540105
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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 | The University of Electro-Communications |
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Principal Investigator |
ANDO Kiyoshi The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (20096944)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIGAMI Yoshiyasu The University of Electro-Communications, Faculty of Electro-Communications, Associate Professor, 電気通信学部, 助教授 (50262374)
KAWARABAYASHI Ken-ichi Tohoku University, Graduate School of Information Science, Research Associate, 大学院・情報科学研究科, 助手 (40361159)
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| Project Period (FY) |
2002 – 2004
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| Keywords | graph theory / discrete optimization / algorithm / computational geometry / discrete geometry / combinatorial geometry / combinatorics / extremal graph theory |
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| Research Abstract |
From an arrangement of points on the plane, we construct a tree joining points by straight line segments, then We call the resulting tree a geometric tree of the arrangement of points. We gave an upper bound on the crossing number of three geometric trees in terms of n each vertex set of which is the subset of each color points sets of a given arrangement of n points with three colors.
For a vertex x of a tree, the number of leafs adjacent with x is called the leaf degree of x. We gave a necessary and sufficient condition for a connected graph to have a spanning tree whose maximum leaf degree is not exceed a given number.
We showed that if both a graph and its complement are contraction critically κ-connected, then the square of its order is not exceed κ^3, also we showed the sharpness of this bound.
An edge e of a 5-connected graph is called trivially noncontractible if there is a vertex of degree 5 which is adjacent, with both end vertices of e. We showed that a contraction critically 5-connected graph of order n has at least n/2 trivially noncontractible edges.
We proved that a 4-connected graph with m vertices of degree greater than 4 has at least m 4-contractible edges.
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[Journal Article] Vertex-disjoint cycles containing specified vertices in a bipartite graph.2004
Author(s)
Chen, Guantao, Enomoto, Hikoe, Kawarabayashi, Ken-ichi, Ota, Katsuhiro, Lou, Dingjun, Saito, Akira
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Journal Title
J.Graph Theory 46, no.3
Pages: 145-165
Description
「研究成果報告書概要(欧文)」より
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[Journal Article] Cycles having the same modularity and removable edges in 2-connected graphs.2003
Author(s)
Ando, Kiyoshi, Hagita, Mariko, Kaneko, Atsushi, Kano, Mikio, Kawarabayashi, Ken-ichi, Saito, Akira
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Journal Title
Discrete Math. 265, no.1-3
Pages: 23-30
Description
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[Journal Article] On separable self-complementary graphs.2002
Author(s)
Kawarabayashi, Ken-ichi, Nakamoto, Atsuhiro, Oda, Yoshiaki, Ota, Katsuhiro, Tazawa, Shinsei, Watanabe, Mamoru
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Journal Title
Discrete Math. 257, no.1
Pages: 165-168
Description
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