Independent sets in classes related to chair-free graphs

Abstract

The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. MWIS is known to be NP-complete in general, but solvable in polynomial time in classes of Si,j,k-free graphs, where Si,j,k is the graph consisting of three induced paths of lengths i, j, k with a common initial vertex. The complexity of the MWIS problem for S1,2,2-free graphs, and for S1,1,3-free graphs are open. In this paper, we show that the MWIS problem can solved in polynomial time for (S1,2,2, S1,1,3, co-chair)-free graphs, by analyzing the structure of the subclasses of this class of graphs. This extends some known results in the literature.