Weighted independent sets in a subclass of P6-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 P-6-free graphs is unknown. In this note, we show that the MWIS problem can be solved in time O(n(3)m) for (P-6, banner)-free graphs by analyzing the structure of subclasses of these class of graphs. This extends the existing results for (P-5, banner)-free graphs, and (P-6, C-4)-free graphs. Here, Pt denotes the chordless path on t vertices, and a banner is the graph obtained from a chordless cycle on four vertices by adding a vertex that has exactly one neighbor on the cycle. (C) 2015 Elsevier B.V. All rights reserved.