On K1,k-factorization of bipartite multigraphs

A K-1,K-k-factorization of lambda K-m,K-n is a set of edge-disjoint K-1,K-k-factors of lambda K-m,K-n, which partition the set of edges of lambda K-m,K-n. In this paper, it is proved that a sufficient condition for the existence of K-1,K-k-factorization of lambda K-m,K-n, whenever k is any positive integer, is that (1) m <= kn, (2) n <= km, (3) km-n equivalent to kn-m equivalent to 0 (mod (k(2)-1)) and (4) lambda(km-n)(kn-m) equivalent to 0 (mod k(k-1)(k(2)-1)(m+n)).