论文标题
$ c_ {4} $ - $ k_ {m，n} $的$λ$ -fold线图的分解
A $C_{4}$-decomposition of the $λ$-fold line graph of $K_{m,n}$
论文作者
论文摘要
许多论文研究了完整图和完整的两部分图的线图（$λ$折线图）的小循环分解。特别是，Colby和Rodger获得了存在$ C_ {4} $的必要条件 - $ K_ {N} $的$λ$ - 折线图的分解，以及Ganesamurthy和Ganesamurthy和Paulraja完全确定了$ n $和$λ$的$λ$ -fold line chage $λ$ k_}的值$ C_ {5} $ - 分解。在本文中，我们获得了存在$ C_ {4} $的必要条件 - $ K_ {m，n} $的$λ$ - 折线的分解。
The small cycle decompositions of line graph ($λ$-fold line graph) of complete graphs and complete bipartite graphs are studied by many papers. In particular, Colby and Rodger obtained necessary and sufficient conditions for the existence of a $C_{4}$-decomposition of the $λ$-fold line graph of $K_{n}$, and Ganesamurthy and Paulraja completely determined the values of $n$ and $λ$ for which the $λ$-fold line graph of $K_{n}$ has a $C_{5}$-decomposition. In this paper, we obtain the necessary and sufficient condition for the existence of a $C_{4}$-decomposition of the $λ$-fold line graph of $K_{m,n}$.
