1996 Fiscal Year Final Research Report Summary
GENERAL RESEARCH OF GRAPH THEORY
| Project/Area Number |
07304016
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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 | 総合 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | IBARAKI UNIVERSITY |
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Principal Investigator |
KANO Mikio IBARAKI UNIVERSITY,FACULTY OF ENGINEERING,PROFESSOR, 工学部, 教授 (20099823)
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| Co-Investigator(Kenkyū-buntansha) |
EGAWA Yoshimi TOKYO SCIENCE UNIVERSITY,FACULTY OF SCI.ASSOCIATE PROF., 理学部, 助教授 (70147502)
ANDO Kiyoshi UNIVERSITY OF ELECTRO-COMMUNICATIONS,FACULTY OF E-C,ASSOCIATE PROF., 電気通信学部, 助教授 (20096944)
MAEHARA Hiroshi RYUKYU UNIVERSITY,FACULTY OF EDUCATION,PROFESSOR, 教育学部, 教授 (60044921)
BANNAI Eiichi KYUSHU UNIVERSITY,FACULTY OF SCIENCES,PROFESSOR, 数理科学研究科, 教授 (10011652)
ENOMOTO Hikoe KEIO UNIVERSITY,FACULTY OF ENG.AND SCI., PROFESSOR, 理工学部, 教授 (00011669)
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| Project Period (FY) |
1995 – 1996
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| Keywords | graph theory / algebraic graph theory / topological graph theory / discrete geometry / algorithm / digital image / combinatorics |
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| Research Abstract |
We studied not only graph theory but also its applications and related branches of mathematics. For example, we researched the following problems and obtained the following results.
(1) Problems on (1, f) -odd subgraphs, which are natural generalizaion of matchings of graphs ; (2) Problem on straight-line embedding of graphs onto a given set of points in the plane ; (3) Problem of determining the minimum crossing number when we embed a graph on a book in three pages ; (4) Sufficient conditions for a graph to have a long cycle ; (5) Counting the number of 4-cycles in a directed graph without 3-cycles ; (6) We prove that for an integer k>=3, every graph with minimum degree at least 2k and with order at least g (k) contains vertex disjoint k cycles of the same length ; (7) We obtain a sufficient condition for a triangulation of Klein bottle to have Hamilton cycle, and study the equivalence of triangulations of Klein bottle under diagonal tranformations ; (8) A sufficient degree condition for a graph to have a cycle possessing a certain given property ; (9) The bandwidth of a graph plays an important role in matrix theory. We determine the upper bound of the bandwidths of trees.
We also studied algebraic graph theory, combinatorics, discrete geometry, algorithm theory, theory and algorithm for digital images, and mathematical theory of machine discovery. For example, we researched spin models, and detemine the primitive symmetric association schemes with m_1=3 ; and gave an effective algorithm for detecting every line component contained in a digital image by making use of thoretical studies.
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