| Project/Area Number |
04302011
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Keio University |
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Principal Investigator |
ENOMOTO Hikoe Keio Univ., Mathematics, Prof., 理工学部, 教授 (00011669)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Akira Nihon Univ., Mathematics, Assoc.Prof., 文理学部, 助教授 (90186924)
NEGAMI Seiya Yokohama Nat.Univ., Education, Assoc.Prof., 教育学部, 助教授 (40164652)
NISHIZEKI Takao Tohoku Univ., Electoronics, Prof., 工学部, 教授 (80005545)
BANNAI Eiichi Kyushu Univ., Mathematics, Prof., 理学部, 教授 (10011652)
MAEHARA Hiroshi Ryukyu Univ., Education, Prof., 教育学部, 教授 (60044921)
今井 浩 東京大学, 理学部, 助教授 (80183010)
江川 嘉美 東京理科大学, 理学部, 助教授 (70147502)
加納 幹雄 明石高専, 助教授 (20099823)
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| Project Period (FY) |
1992 – 1994
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| Project Status |
Completed (Fiscal Year 1994)
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| Budget Amount *help |
¥9,000,000 (Direct Cost: ¥9,000,000)
Fiscal Year 1994: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1993: ¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 1992: ¥3,700,000 (Direct Cost: ¥3,700,000)
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| Keywords | Combinatorics / Cycles and paths of graphs / Connectivity / Graph embedding / Algorithms / Computational Geometry / Spin models / Association schemes / 分割問題 / 閉路 / 次数 / 埋め込み / 連結度 / 双対グラフ / 指標表 |
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| Research Abstract |
We obtained high level results in graph theory.In particular, we proved the existence of k-facors, connected [2, k]-factors, long cycles or hamiltonian cycles assuming various kinds of connectivity (vertex-connectivity, edge-connectivity, toughness, binding number etc.). For example, we proved that with few exceptios the length of a logest cycle is at least the length of a logest path-1 if the sum of degrees of three independent vertices is at least the order of the graph. There is a strong connection between geometric properties of a surface and those of graphs enbedded in it. Geometric dual of a planar graph is well-defined, but it is not obvious what is the dual of graphs enbedded in other surfaces. We investigated duals of graphs enbedded in a projective plane. We also obtained properties of triangulations and quadrangulations of various surfaces, and decided the number of equivalence classes of such graphs under fundamental deformations. On algebraic combinatorial theory, we studied distance-regular graphs, association schemes, spin models, and Hadamard matrices. We clarified the relation of spin models and association schemes, and the properties of the character table of an association scheme. Also, we get various results on finite geometris, arrangements of lines or hyperplanes, computational geometries, and graph algorithms.
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