A Note on Bound Graphs and Clique Covers

McMorris, Zaslavsky, and Diny give characterizations of upper bound graphs and double bound graphs in terms of edge clique covers, that is, a family of maximal complete subgraphs that covers all edges. Lundgren and Maybee give a characterization of upper bound graphs using a concept of non-maximal complete subgraphs. In this paper, we present characterizations of double bound graphs and semi-bound graphs in terms of edge covers of non-maximal complete subgraphs.