Abstract
In this paper, it is shown that a necessary and sufficient condition for the existence of aC k-factorization ofK m,n is (i)m = n ≡ 0 (mod 2), (ii)k ≡ 0 (mod 2),k ≥ 4 and (iii) 2n ≡ 0 (modk) with precisely one exception, namely m =n = k = 6.
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Horton, J.D., Roy, B.K., Schellenberg, P.J., Stinson D.R.: On decomposing graphs into isomorphic uniform 2-factors, Ann. Discrete Math.27, 297–320 (1985)
Sotteau, D.. Decomposition ofK m, n (K *m,n ) into cycles (circuits) of length 2k. J. Comb. Theory (B)30, 75–81 (1981)
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Enomoto, H., Miyamoto, T. & Ushio, K. C k -factorization of complete bipartite graphs. Graphs and Combinatorics 4, 111–113 (1988). https://doi.org/10.1007/BF01864159
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DOI: https://doi.org/10.1007/BF01864159