| 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)
金子 篤司 工学院大学, 工学部, 助教授 (30255608)
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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 |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2004: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
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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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