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Embedding and Partition of Graphs

Research Project

Project/Area Number 14540134
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHIROSHIMA UNIVERSITY (2003-2004)
Keio University (2002)

Principal Investigator

ENOMOTO Hikoe  Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00011669)

Co-Investigator(Kenkyū-buntansha) OTA Katsuhiro  Keio University, Faculty of Science and Technology, Professor, 理工学部, 教授 (40213722)
MATSUMOTO Makoto  Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70231602)
江端 満彦  広島大学, 大学院・理学研究科, 助手 (70363041)
Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsgraph / cycle / factor / decree condition / independence number / connectivity / 次数条件 / 因子分解 / (g, f)-因子 / 分割 / 孤立点 / 成分因子 / 彩色数 / リスト彩色数 / 直径
Research Abstract

(1)In 1997, Brandt and others proved that a graph G of order at least 4k and the degree sum of nonadjacent vertices at least |V(G)| can be partitioned into k disjoint cycles. This result is generalized in several ways. We weakened the degree sum assumption to |V(G)|-k+1 by allowing degenerated cycles (edges and isolated vertices). We also obtained sufficient conditions on the minimum degree to assure that each cycle passes through a specified vertex. We also solved the problem in which each cycle passes through a specified vertex or a specified edge. Furthermore, we solved the problem for bipartite graphs.
(2)Erdos-Chvatal theorem says that if the independence number is not larger than the connectivity, the graph contains a Hamiltonian cycle. We generalized this result to the existence of a long cycle.
(3)We investigated the maximum order of a graph without k disjoint cycles and the independence number is at most α.
(4)We proved that if G is an (mg+m-1,mf-m+1)-graph and if k≦g(x)≦f(x) for any vertex x of G,G can be factorized into (g,f)-factors in which each factor contains k specified edges.

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (22 results)

All 2004 2003 Other

All Journal Article (12 results) Publications (10 results)

  • [Journal Article] Partition of a graph into cycles and degenerated cycles2004

    • Author(s)
      H.Enomoto
    • Journal Title

      Discrete Math. 276

      Pages: 177-181

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Long cycles in triangle-free graphs with prescribed independence number and connectivity2004

    • Author(s)
      H.Enomoto
    • Journal Title

      J.Combinatorial Theory Ser.B 91

      Pages: 43-55

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Vertex-disjoint cycles containing specified vertices in a bipartite graphs2004

    • Author(s)
      G.Chen
    • Journal Title

      J.Graph Theory 46

      Pages: 145-166

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Long cycles in triangle-free graphs with prescribed independence number and connectivity2004

    • Author(s)
      H.Enomoto
    • Journal Title

      J.Combin.Theory Ser.B 91

      Pages: 43-55

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Vertex-disjoint cycles containing specified vertices in a bipartite graph2004

    • Author(s)
      G.Chen
    • Journal Title

      J.Graph Theory 46

      Pages: 145-166

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Long cycles in triangle-free graphs with prescribed independence number and connectivity2004

    • Author(s)
      H.Enomoto, A.Kaneko, A.Saito
    • Journal Title

      Discrete Mathematics 276

      Pages: 177-181

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Vertex-disjoint cycles containing specified vertices in a bipartite graph2004

    • Author(s)
      G.Chen, H.Enomoto他
    • Journal Title

      J.Graph Theory 46

      Pages: 145-166

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On minimally 3-connected graphs on a surface2004

    • Author(s)
      K.Ota
    • Journal Title

      A KCE International J.of Graphs and Combinatorics 1

      Pages: 29-33

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Practical fast algorithm for finite field arithmetics using groupings2004

    • Author(s)
      M.Matsumoto, S.Tagami
    • Journal Title

      Hiroshima Math.J. 34

      Pages: 201-210

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Two-factors each component of which contains a specified vertex2003

    • Author(s)
      Y.Egawa
    • Journal Title

      J.Graph Theory 43

      Pages: 188-198

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Diagonal flips in Hamiltonian triangulations on the sphere2003

    • Author(s)
      R.Mori
    • Journal Title

      Graphs and Combinatorics 19

      Pages: 413-418

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Diagonal flips in Hamiltonian triangulations on the sphere2003

    • Author(s)
      R.Mori
    • Journal Title

      Graphs Combin. 19

      Pages: 413-418

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] Y.Egawa, H.Enomoto 他: "Two-factors each component of which contains a specified vertex"J.Graph Theory. 43. 188-198 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Enomoto, H.Li: "Partition of a graph into cycles and degenerated cycles"Discrete Math.. 276. 177-181 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Ken-ichi Kawarabayashi, Atsuhiro Nakamoto, Katsuhiro Ota: "Subgraphs of graphs on surfaces with high representativity"Journal of Combinatorial Theory Series B. 89. 207-229 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] R.Mori, A.Nakamoto, K.Ota: "Diagonal Flips in Hamiltonian Triangulations on the Sphere"Graphs and Combinatorics. 19. 413-418 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Enomoto, T.Nakamigawa: "On the decomposition dimension of trees"Discrete Mathematics. 252. 219-225 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Enomoto, K.Ohba, K.Ota, J.Sakamoto: "Choice number of some complete multi-partite graphs"Discrete Mathematics. 244. 55-66 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Egawa, H.Enomoto, N.Tokushige: "Graph decompositions through prescribed vertices without isolates"Ars Combinatoria. 62. 189-205 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Kawarabayashi, H.Matsuda, Y.Oda, K.Ota: "Path factors in cubic graphs"J. Graph Theory. 39. 188-193 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Hagita, Y.Oda, K.Ota: "The diameters of some transition graphs constracted from Hamilton cycles"Graphs and Combinatorics. 18. 105-117 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Kawarabayashi, K.Ota, A.Saito: "Hamilton cycles in n-extendable graphs"J. Graph Theory. 40. 75-82 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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