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 .
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Revised: May 7, 1999
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Chen, G., Faudree, R., Gould, R. et al. Cycles in 2-Factors of Balanced Bipartite Graphs. Graphs Comb 16, 67–80 (2000). https://doi.org/10.1007/s003730050004
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DOI: https://doi.org/10.1007/s003730050004