Weighted independent sets in classes of $P_6$-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. The complexity of the MWIS problem for $P_6$-free graphs, and for $S_{1,2,2}$-free graphs are unknown. In this note, we give a proof for the solvability of the MWIS problem for ($P_6$, $S_{1,2,2}$, co-chair)-free graphs in polynomial time, by analyzing the structure and the MWIS problem in various subclasses of ($P_6$, $S_{1,2,2}$, co-chair)-free graphs. These results extend some known results in the literature.