Maximum weight independent sets in classes related to claw-free graphs

The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. The complexity of the MWIS problem for S1,1,3-free graphs, and for S1,2,2-free graphs is unknown. We show that the MWIS problem in (S1,1,3, banner)-free graphs, and in (S1,2,2, bull)-free graphs can be solved in polynomial time. These results extend some known results in the literature.