| Co-Investigator(Kenkyū-buntansha) |
EGAWA Yoshimi Sci. Univ.of Tokyo, Applied Mathematics, Professor, 理学部, 教授 (70147502)
OTA Katsuhiro Keio University, Mathematics, Assistant Professor, 理工学部, 助教授 (40213722)
JIMBO Masakazu Keio University, Mathematics, Professor, 理工学部, 教授 (50103049)
KANEKO Atsushi Kogakuin University, Computer Science, Assistant Professor, 工学部, 助教授 (30255608)
SAITO Akira Nihon University, Applied Mathematics, Assistant Professor, 文理学部, 教授 (90186924)
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| Research Abstract |
・A 3-connected graph of order at least t can be partitioned into connected subgraphs of order at least t and at most 2t-1. Using this result, we can show that a 3-connected graph of order at least t contains a connected subgraph of order t whose degree sum is at most 8t-1.
・For a 3-page book embedding of a graph of order n and size m, the order of the minimum number of edge-crossings orer the spine is O (m logィイD1nィエD1).
・Let G be a k-connected graph of order p, p-n is even, α is a real number with ィイD71(/)2ィエD7≦α≦1, and suppose |Na(a)|>α(p-2k+n-2)+k for any indegredant subset A of G with |A|=[α(k-n+2)]. Then G is n-factor-critical.
・Let G be a balanced bipartite graph of order 2n, K≧2, n≧2k.. Suppose σィイD21ィエD2,(G1)≧ max {n+k, [ィイD72n-1(/)3ィエD7]+2k} or δ(G)≧ max {[ィイD7n+k(/)2ィエD7],[ィイD72n+4k(/)5ィエD7]}. Then for any independent edges. EィイD21ィエD2,---, eィイD2kィエD2, G can be partitioned into disjoint cycles CィイD21ィエD2,----, CィイD2kィエD2 satisfying eィイD2iィエD2 εE (GィイD2iィエD2) 1≦I≦k..
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