| Project/Area Number |
09304020
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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) |
EGAWA Yoshimi Science University of Tokyo, Faculty of Science, Professor, 理学部, 教授 (70147502)
KANO Mikio Ibaraki University, Faculty of Engineering, Professor, 工学部, 教授 (20099823)
WATANABE Mamoru Kurashiki University of Science and the Arts, Faculty of Industrial Science and, 産業科学技術学部, 教授 (90068916)
ENOMOTO Hikoe Keio University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (00011669)
MAEHARA Hiroshi Ryukyu University, Faculty of Education, Professor, 教育学部, 教授 (60044921)
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| Project Period (FY) |
1997 – 1998
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| Keywords | graph thory / discrete geometry / combinatorial geometry / algorithm / computatinal geome- / combinatorics / topological graph thory / discrete optimization |
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| Research Abstract |
Ando and Kaneko showed that the edge version k-wide diameter of a k edge-connected graph with diameter d is O(d^k) and this degree bound is sharp. Maehara showed that a trefoil knot can be constructed by 15 mutually disjoint unit balls in 3 dimensinal space and a trefoil knot can be constructed by 12 mutually disjoint two different sized balls. Also he proved that the minimum number of mutually disjoint unit balls between two parallel planes between which distance is 2+ROO<2> to construct a knot is 16. Enomoto studied graph decom-position problem and found a good sufficient condition for a graph to have a prescribed order decomposition without isolated vertices. Watanabe introduced a new type of visibility graphs and disproved a Mirzaian's conjecture. Okamura found a new sufficient condition for a graph to have a six-terminal multicommodity flow. Yamasaki studied reversed positional games and got some properties of them. Also Yamasaki introduced an invariant to discriminate 1-factoriza
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tions of a complete graph. Kaneko and Kano showed a forest can be line embedded into plane if either the forest consists of two rooted trees, each component of it is star or each component of it is rooted tree of the same order. Furthermore they gave polynomial time algolithms for these graph embedding problems. Applying some techniques of computatinal geometry, Asano propose a. new high speed algolithm for geometric representation of a digital image. Jimbo studied cyclic resolvability of cyclic Steiner 2-designs and nested directed BIB designs. Ando and Egawa proved. that the number of edges of a diameter-2-critical graph of order n <greater than or equal> 23 is greater than or equal to (5n - 17)/2. Negami completed the classification of reduced triangulations on Klein bottle. Saito found new sufficient conditions for a claw-free graph to have a hamiltonian cycle. Also he investigated the relaton between Ryj_cek closure and factors in a graph. Tsuchiya showed that there is a strong relation among upper bound graphs, edge clique cover of a graph and order ideal of a poset. Ota proved that a graph of order <greater than or equal> 4k +6 with the minimum degree <greater than or equal> k +2 has k vertex disjoint K_<1,3-> Nishimura proved a new recursive theorem on n-extendibility of a graph. Ishigami proved Wang's conjecture on cycle covering and Ore type degre Less
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