On K1, k-factorizations of a complete bipartite graph

Abstract We present a necessary condition for a complete bipartite graph Km,n to be K1,k-factorizable and a sufficient condition for Km,n to have a K1,k-factorization whenever k is a prime number. These two conditions provide Ushio's necessary and sufficient condition for Km,n to have a K1,2-factorization.