Strongly Perfect Graph

A graph is strongly perfect if every induced subgraph  has an independent vertex set meeting all maximal cliques of  (Berge and Duchet 1984, Ravindra 1999).

Every strongly perfect graph is perfect, but the converse is not necessarily true.

Every -free graph (i.e., every graph not containing the path graph  as a vertex-induced subgraph), is strongly perfect (Ravindra 1999).

REFERENCES

Berge, C. and Duchet, P. "Strongly Perfect Graphs." Ann. Disc. Math. 21, 57-61, 1984.

Ravindra, G. "Some Classes of Strongly Perfect Graphs." Disc. Math. 206, 197-203, 1999.

Wang, H. Y. "Which Claw-Free Graphs Are Strongly Perfect?" Disc. Math. 306, 2602-2629, 2006.