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 \(2K_{2m}\).