Weighted independent sets in classes of P6-free graphs

T. Karthick (1) , Frédéric Maffray (2)

1 Indian Statistical Institute [Chennai]
2 G-SCOP_OC - Optimisation Combinatoire

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 P6-free graphs, and for S1,2,2-free graphs are unknown. In this note, we give a proof for the solvability of the MWIS problem for (P6, S1,2,2, co-chair)-free graphs in polynomial time, by analyzing the structure and the MWIS problem in various subclasses of (P6, S1,2,2, co-chair)-free graphs. These results extend some known results in the literature.

Domaines: Mathématique discrète [cs.DM]

T. Karthick, Frédéric Maffray. Weighted independent sets in classes of P6-free graphs. Discrete Applied Mathematics, 2016, 9th International Colloquium on Graph Theory and Combinatorics, 2014, Grenoble, 209, pp.217-226. ⟨10.1016/j.dam.2015.10.015⟩. ⟨hal-01332694⟩