Cycles in 2-Factors of Balanced Bipartite Graphs

In the study of hamiltonian graphs, many well known results use degree conditions to ensure su1⁄2cient 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 1U k U jV…G†j 4 . 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 nVmax 51; k 2 ‡ 1 .