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.