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 graphG, but also the existence of a 2-factor with exactlyk 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 exactlyk cycles in a balanced bipartite graph of order 2n with.

Authors and Affiliations

1.  Georgia State University, Atlanta, GA 30303, USA, , , , , , GE

   Guantao Chen

2.  University of Memphis, Memphis, TN 38152, USA, , , , , , US

   Ralph J. Faudree

3.  Emory University, Atlanta GA 30322, USA, , , , , , US

   Ronald J. Gould

4.  University of Louisville, Louisville, KY 40292, USA, , , , , , US

   Michael S. Jacobson

5.  Drew University, Madison NJ 07940, USA, , , , , , US

   Linda Lesniak

Revised: May 7, 1999

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