A graph is strongly perfect if every induced subgraph (Formula presented.) of it has a stable set that meets every maximal clique of (Formula presented.). A graph is claw-free if no vertex has three pairwise nonadjacent neighbors. The characterization of claw-free graphs that are strongly perfect by a set of forbidden induced subgraphs was conjectured by Ravindra in 1990 and was proved by Wang in 2006. Here we give a shorter proof of this characterization.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- claw-free graphs
- induced subgraphs
- perfect graphs
- strongly perfect graphs