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2004 Fiscal Year Final Research Report Summary

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)
Project Period (FY) 2002 – 2004
Keywordsgraph / cycle / factor / decree condition / independence number / connectivity
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.

  • Research Products

    (8 results)

All 2004 2003

All Journal Article (8 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 2006-07-11  

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