A star cover of a graph is a spanning subgraph for which each component is a star, K1,m. For edge weighted graphs, necessary conditions for a star cover to have minimum weight are known. These conditions are expressed in terms of the absence of a certain set of subgraphs (forbidden subgraphs). However, these necessary conditions are not sufficient for a star cover to have minimum weight. The inclusion of further subgraphs leads to a set of forbidden subgraphs whose absence is sufficient (but not necessary) for a star cover to have minimum weight
