Some Results on $4$-Cycle Packings

Abstract

A packing of a graph $G$ is a set of edge-disjoint $4$-cycles in $G$ and a maximum packing of $G$ with $4$-cycles is a packing which contains the largest number of $4$-cycles among all packings of $G$. In this paper, we obtain the maximum packing of certain graphs such as $K_{2m+1}–H$ where $H$ is a $2$-regular subgraph, $K_{2m}–F$ where $F$ is a spanning odd forest of $K_{2m}$, and $2K_{2m}–L$ where $L$ is a $2$-regular subgraph of $2K_{2m}$.