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Combinatorial Theory

Research Project

Project/Area Number 04302011
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKeio University

Principal Investigator

ENOMOTO Hikoe  Keio Univ., Mathematics, Prof., 理工学部, 教授 (00011669)

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)
Project Period (FY) 1992 – 1994
Project Status Completed (Fiscal Year 1994)
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)
KeywordsCombinatorics / 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
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.

Report

(4 results)
  • 1994 Annual Research Report   Final Research Report Summary
  • 1993 Annual Research Report
  • 1992 Annual Research Report
  • Research Products

    (40 results)

All Other

All Publications (40 results)

  • [Publications] H.ENOMOTO,M.Kano: "Disjoint odd integer subsets having a constant even sum" Discrete Mathematics. 137. 189-193 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] M.Deza,H.Maehara: "A Few Applications of Negative-Type Inequalities" Graphs and Combinatorics. 10. 255-262 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] E.Bannai,F.Jaeger 他: "Classification of small spin models" Kyushu J.Mathematics. 48. 185-200 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] N.Kanamaru,T.Nishizeki T.Asano: "Efficient enumeration of grid points in a convex polygon and its application to integer programming" International Journal of Computational Geometry&Applications. 4. 69-85 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] S.Negami,M.Tsuchiya: "Manifold posets" J.Yokohama National University Sec.I. 41. 23-32 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] G.Chen,A.Saito: "Graphs with a Cycle of Length Divisible by Three" Journal of Combinatorial Theory,Series B. 60. 277-292 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] E.Hirowatari, S.Arikawa: "INCORPORATING EXPLANATION-BASED GENERALIZATION WITH ANALOGICAL REASONING" Bull.of Inform.and Cybern. 26. 13-33 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Asano, T.Tokuyama: "Partial Construction of an Arrangement of Lines and Its Application to Optimal Partitioning of Bichromatic Point Set" IEICE TRANS.on Fund.of Electronics, Commun.and Computer Sciences. 595-600 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] N.Kanamaru, T.Nishizeki, T.Asano: "EFFICIENT ENUMERATION OF GRID POINTS IN A CONVEX POLYGON AND ITS APPLICATION TO INTEGER PROGRAMMING" International J.of Computational Geometry & Applications. 4. 69-85 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Asano, L.J.Guibas, T.Tokuyama: "WALKING IN AN ARRANGEMENT TOPOLOGICALLY" International J.of Computational Geometry & Applications. 4. 123-151 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] E.Bannai, E.Bannai: "Modular invariance of the character table of the Hamming association scheme H(d, q)" J.of Number Theory. 47. 79-92 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] E.Bannai, E.Bannai: "Spin models on finite cyclic groups" J.of Algebraic Combinatorics. 3. 243-259 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] E.Bannai, F.Jaeger, A.Sali: "Classification of small spin models" Kyushu J.of Math.48. 185-200 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] H.Enomoto, A,Kaneko: "The Condition of Beineke and Harary on Edge-Disjoint Paths Some of Which are Openly Disjoint" Tokyo J.of Mathematics. 17. 355-357 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] H.Enomoto: "Graph Decompositions without Isolated Vertices" J.of Combin.Theory(B). 63. 111-124 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] H.Enomoto, M.Kano: "Disjoint odd integer subsets having a constant even sum" Discrete Math.137. 189-193 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] S.Tani, H.Imai: "A Recordering Operation for an Ordered Binary Decision Diagram and an Extended Framework for Combinatorics of Graphs" Algorithms and Computation. 834. 575-583 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] M.Inaba, N.Katoh, H.Imai: "Applications of Weighted Voronoi Diagrams and Randomization to Variance-Based k-Clustering" Proc.of Genome Inform.Workshop. 332-339 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Ikeda, H.Imai: "Fast A^* Algorithms for Multiple Sequence Alignment" Proc.of The Tenth Ann.Symp.on Comput.Geom.90-99 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] M.Deza, H.Maehara: "Projecting a Simplex onto Another One" European J.Combin.15. 13-16 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] S.Negami, M.Tsuchiya: "Manifold posets" J.Yokohama Nat.Univ. 41. 23-32 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] G.Chen, A.Saito: "Graphs with a Cycle of Length Divisible by Three" J.of Combin.Theory (B). 60. 277-292 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] H.Enomoto,M.Kano: "Disjoint odd integer subsets having a constant even sum" Discrete Mathematics. 137. 189-193 (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] M.Deza,H.Maehara: "A Few Applications of Negative-Type Inequalities" Graphs and Combinatorics. 10. 255-262 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] E.Bannai,F.Jaegar 他: "Classification of small spin models" Kyushu J.Mathematics. 48. 185-200 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] N.Kanamaru,T.Nishizeki,T.Asano: "Efficient enumeration of grid points in a convex polygon and its application to integer programming" International Journal of Computational Geometry & Applications. 4. 69-85 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] S.Negami,M.Tsuchiya: "Manifold posets" J.Yokoyama Natronal University Sec.I. 41. 23-32 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] G.Chen,A.Saito: "Graphs with a Cycle of Length Divisible by Three" Journal of Combinational Theory,Series B. 60. 277-292 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] H.Enomoto: "The Schur indices of the irreducible characters G_2(2^n)" Proc.Japan Academy. 69A. 350-352 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] E.Bannai: "Association schemes and fusion algebras(ar introduction)" J.of Algebraic combinatorics. 2. 327-344 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Y.Egawa: "Edge‐disjoint hamiltoniar cycles in graphs of Ore type" SUT J.Math.29. 15-50 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] D.Archdeacon and S.Negami: "The construction of self‐dual projective polyhedra" J.Combinatorial Theory. B59. 122-131 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] N.Dean ,L.Lesniak and A.Saito: "Cycles of length 0 modulo 4 in graphs" Discrete Math.121. 37-49 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] S.Hasegawa,H.Imai and M.Ishiguro: "E‐Approximations of k‐Label Spaces" Lecture Notes in Computer Science. Vol.744. 288-299 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] H.Enomoto: "A word problem in Artin semigroups" Discre te Mathematics. 104. 159-166 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] K.Ota(W.Mc Cuaig): "Contractible triples in 3-connected graphs" Journal of Conbinatorial theory Series B.

    • Related Report
      1992 Annual Research Report
  • [Publications] E.Bannai: "Moular invariance of the character table of the Hamming association scheme H(d,g)" Journal of Number Theory.

    • Related Report
      1992 Annual Research Report
  • [Publications] S.Negami: "Projective-planar graphs with eren duals" Journal of Graph Theory. 16. 287-295 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] A.Saito: "Cycles of length 2 mod 3 in graphs" Dixcrete Mathematics. 101. 285-289 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] M.kano: "Binding numbers and f-factors of graphs" journal of Combinatorial theory Series B. 54. 213-221 (1992)

    • Related Report
      1992 Annual Research Report

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Published: 1992-04-01   Modified: 2016-04-21  

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