Well-Covered Claw-Free Graphs

We prove the existence of a polynomial time algorithm to tell whether a graph, with no induced subgraph isomorphic toK1.3, is well covered. A graph is well-covered if all its maximal independent sets are of the same cardinality. The problem is known to be polynomialy solvable where the input graph is a line graph and it isNP-hard for the larger family of all graphs which do not contain an induced subgraph isomorphic toK1,4.