Maximum weight independent sets in (P6,co-bannerP6,co-banner)-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. Being one of the most investigated problem on graphs, it is well known to be NPNP-complete and hard to approximate. Several graph classes for which MWIS can be solved in polynomial time have been introduced in the literature. This note shows that MWIS can be solved in polynomial time for (P6,co-bannerP6,co-banner)-free graphs – where a P6P6 is an induced path of 6 vertices and a co-banner is a graph with vertices a,b,c,d,ea,b,c,d,e and edges ab,bc,cd,ce,deab,bc,cd,ce,de – so extending different analogous known results for other graph classes, namely, P4P4-free, 2K22K2-free, (P5,co-bannerP5,co-banner)-free, and (P6,triangleP6,triangle)-free graphs. The solution algorithm is based on an idea/algorithm of Farber (1989) [10], leading to a dynamic programming approach for MWIS, and needs none of the aforementioned known results as sub-procedure.

► The note deals with the Maximum Weight Independent Set (MWIS) Problem. ► It shows that MWIS can be efficiently solved for (P6,co-bannerP6,co-banner)-free graphs. ► It extends different analogous known results for other graph classes. ► It needs none of the aforementioned known results as sub-procedure. ► It is based on a previous idea of Martin Farber.