Jing SHI, Jian WANG, Bei-liang DU
Let $\lambda K_{m,n}$ be a complete bipartite multigraph with two partite sets having $m$ and $n$ vertices, respectively. A $K_{p,q}$-factorization of $\lambda K_{m,n}$ is a set of $K_{p,q}$-factors of $\lambda K_{m,n}$ which partition the set of edges of $\lambda K_{m,n}$. When $\lambda =1$, Martin, in [Complete bipartite factorizations by complete bipartite graphs, Discrete Math., 167/168 (1997), 461-480], gave simple necessary conditions for such a factorization to exist, and conjectured those conditions are always sufficient. In this paper, we will study the $K_{p,q}$-factorization of $\lambda K_{m,n}$ for $p=1$, to show that the necessary conditions for such a factorization are always sufficient whenever related parameters are sufficiently large.