Ck-factorization of complete bipartite graphs

In this paper, it is shown that a necessary and sufficient condition for the existence of aCk-factorization ofKm,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.