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 $G-G{D}_{\lambda }(H)$, 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 $G-G{D}_{\lambda }(H)$, denoted by $G-LG{D}_{\lambda }(H)$, is a partition of all subgraphs isomorphic to $G$ of $H$ into $G-G{D}_{\lambda }(H)$s. In this paper, we determine the existence spectrums for $K_{2,2}-LG{D}_{\lambda }(K_{m,n})$.