Multidecompositions of the Complete Graph

Abstract

Let \(G\) and \(H\) be a pair of non-isomorphic graphs on fewer than \(m\) vertices. In this paper, we introduce several new problems about decomposing the complete graph \(K_m\) into copies of \(G\) and \(H\). We will assume that at least one of \(G\) or \(H\) is not a cycle. We also begin to examine variations to the problems of subgraph packing, covering, and factorization.