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Graphs and Combinatorics

, Volume 16, Issue 1, pp 67–80 | Cite as

Cycles in 2-Factors of Balanced Bipartite Graphs

  • Guantao Chen
  • Ralph J. Faudree
  • Ronald J. Gould
  • Michael S. Jacobson
  • Linda Lesniak

Abstract.

In the study of hamiltonian graphs, many well known results use degree conditions to ensure sufficient edge density for the existence of a hamiltonian cycle. Recently it was shown that the classic degree conditions of Dirac and Ore actually imply far more than the existence of a hamiltonian cycle in a graph G, but also the existence of a 2-factor with exactly k cycles, where \(\). In this paper we continue to study the number of cycles in 2-factors. Here we consider the well-known result of Moon and Moser which implies the existence of a hamiltonian cycle in a balanced bipartite graph of order 2n. We show that a related degree condition also implies the existence of a 2-factor with exactly k cycles in a balanced bipartite graph of order 2n with \(\).

Keywords

Bipartite Graph Balance Bipartite Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 2000

Authors and Affiliations

  • Guantao Chen
    • 1
  • Ralph J. Faudree
    • 2
  • Ronald J. Gould
    • 3
  • Michael S. Jacobson
    • 4
  • Linda Lesniak
    • 5
  1. 1. Georgia State University, Atlanta, GA 30303, USAGE
  2. 2. University of Memphis, Memphis, TN 38152, USAUS
  3. 3. Emory University, Atlanta GA 30322, USAUS
  4. 4. University of Louisville, Louisville, KY 40292, USAUS
  5. 5. Drew University, Madison NJ 07940, USAUS

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