Large Sets of \(K_{2,2}\)-Decomposition of Complete Bipartite Graphs

Abstract

Let \(H\), \(G\) be two graphs, where \(G\) is a simple subgraph of \(H\). A \(G\)-decomposition of \(H\), denoted by \(G-GD_\lambda(H)\), is a partition of all the edges of \(H\) into subgraphs (called \(G\)-blocks), each of which is isomorphic to \(G\). A large set of \(G-GD_\lambda(H)\), denoted by \(G-LGD_\lambda(H)\), is a partition of all subgraphs isomorphic to \(G\) of \(H\) into \(G-GD_\lambda(H)\)s. In this paper, we determine the existence spectrums for \(K_{2,2}-LGD_\lambda(K_{m,n})\).