%0 Journal Article
%A Jing SHI
%A Jian WANG
%A Bei-liang DU
%T Star-factorization of the Complete Bipartite Multigraphs
%D 2023
%R 10.1007/s10255-023-1044-9
%J 应用数学学报(英文)
%P 239-248
%V 39
%N 2
%X 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.
%U https://applmath.cjoe.ac.cn/jweb_yysxxb_en/CN/10.1007/s10255-023-1044-9