ABSTRACT
Over the years there have been numerous conjectures and open problems dealing with collections of subgraphs of a given graph G where each edge of G belongs to exactly one subgraph in the collection. While many of these conjectures have been verified, others remain unresolved. Collections of subgraphs with this property are often divided into two categories, depending on whether the subgraphs are required to be spanning subgraphs of G.
