Efficient robust algorithms for the Maximum Weight Stable Set Problem in chair-free graph classes

Abstract

Modular decomposition of graphs is a powerful tool for designing efficient algorithms for problems on graphs such as Maximum Weight Stable Set (MWS) and Maximum Weight Clique. Using this tool we obtain O( n· m) time algorithms for MWS on chair- and xbull-free graphs which considerably extend an earlier result on bull- and chair-free graphs by De Simone and Sassano (the chair is the graph with vertices a, b, c, d, e and edges ab, bc, cd, be, and the xbull is the graph with vertices a, b, c, d, e, f and edges ab, bc, cd, de, bf, cf). Moreover, our algorithm is robust in the sense that we do not have to check in advance whether the input graphs are indeed chair- and xbull-free.