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Graphs and Combinatorics

, Volume 16, Issue 1, pp 81–92 | Cite as

Vertex-Disjoint Cycles Containing Specified Edges

  • Yoshimi Egawa
  • Ralph J. Faudree
  • Ervin Györi
  • Yoshiyasu Ishigami
  • Richard H. Schelp
  • Hong Wang

Abstract.

Dirac and Ore-type degree conditions are given for a graph to contain vertex disjoint cycles each of which contains a previously specified edge. One set of conditions is given that imply vertex disjoint cycles of length at most 4, and another set of conditions are given that imply the existence of cycles that span all of the vertices of the graph (i.e. a 2-factor). The conditions are shown to be sharp and give positive answers to conjectures of Enomoto in [3] and Wang in [5].

Keywords: cover, cycle, partition, 2-factor 

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Copyright information

© Springer-Verlag Tokyo 2000

Authors and Affiliations

  • Yoshimi Egawa
    • 1
  • Ralph J. Faudree
    • 2
  • Ervin Györi
    • 3
  • Yoshiyasu Ishigami
    • 4
  • Richard H. Schelp
    • 2
  • Hong Wang
    • 5
  1. 1. Department of Applied Mathematics, Science University of Tokyo, Shinjuku-ku, Tokyo 162-8601, JapanJP
  2. 2. Department of Math. Sciences, University of Memphis, Memphis, TN 38152, USAUS
  3. 3. Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1364 Budapest, HungaryHU
  4. 4. Department of Information and Communication Engineering, University of Electro-Communications, Chofu, Tokyo 182-8585, JapanJP
  5. 5. Department of Mathematics, University of Idaho, Moscow, ID 83844, USAUS

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