The problem of finding a maximum (weight) stable set in a given graph is a well-known NP-hard problem. We present two polynomial-time solutions to the problem, when the input is restricted to particular graph classes.

The first solution deals with the weighted version of the problem for fork-free graphs, and is based on modular decomposition. Secondly, we show how to solve in polynomial time the unweighted case for certain subclasses of planar graphs. To this end, we combine Tarjan's decomposition by clique separators with the technique of finding augmenting graphs.

This is a joint work with Vadim V. Lozin.