Weighted independent sets in a subclass of P6-free graphs

Authors

T. Karthick, Indian Statistical Institute Chennai

Article Type

Research Article

Publication Title

Discrete Mathematics

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 P6-free graphs is unknown. In this note, we show that the MWIS problem can be solved in time O(n3m) for (P6, banner)-free graphs by analyzing the structure of subclasses of these class of graphs. This extends the existing results for (P5, banner)-free graphs, and (P6, C4)-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.

First Page

1412

Last Page

1418

DOI

10.1016/j.disc.2015.12.008

Publication Date

4-6-2016

Comments

Open Access; Bronze Open Access

Recommended Citation

Karthick, T., "Weighted independent sets in a subclass of P6-free graphs" (2016). Journal Articles. 4524.
https://digitalcommons.isical.ac.in/journal-articles/4524