The characterization of strongly perfect graphs by forbidden induced subgraphs

Let $G$ be a graph. A graph is strongly perfect if every induced subgraph has a stable set meeting every nonempty maximal clique. An odd hole is an induced cycle of odd length, and an antihole is the complement of an induced cycle; the five graphs labeled I, II, III, IV, and V are the graphs shown in Figure. The strongly perfect graph conjecture. A graph $G$ is strongly perfect if and only if it contains no odd holes, no antiholes of length at least six, and none of the graphs I, II, III, IV, or V. The conjecture would provide a forbidden-induced-subgraph characterization of strongly perfect graphs, extending the known characterization for claw-free strongly perfect graphs; the general characterization remains open.