A acyclic digraph $G$ is said to have the Gallai-Milgram-Linial property for clique covers if for every induced subgraph $H$ and every clique cover of vertices of $H$ with sink-set $S$, there is a vertex cover of $H$ by $c$ cliques whose sinks come from $S$, where $c$ is the largest number of pairwise nonadjacent vertices in $G$. The author gives the necessary and sufficient conditions that acyclic digraphs have the Gallai-Milgram-Linial property. Five forbidden subgraphs are presented to establish the results.
Reviewer: D.P.Brown (Carbondale)