On 2-factors containing 1-factors in bipartite graphs

Moon and Moser (Israel J. Math. 1 (1962) 163-165) showed that if G is a balanced bipartite graph of order 2n and minimum degree 0>~(n + 1)/2, then G is hamiltonian. Recently, it was shown that their well-known degree condition also implies the existence of a 2-factor with exactly k cycles provided n~> max{52,2k -~ + 1}. In this paper, we show that a similar degree condition implies that for each perfect matching M, there exists a 2-factor with exactly k cycles including all edges of M. @ 1999 Published by Elsevier Science B.V. All rights reserved