On the threshold-width of graphs
Combinatorics
2012-11-01 v1 Discrete Mathematics
Abstract
The GG-width of a class of graphs GG is defined as follows. A graph G has GG-width k if there are k independent sets N1,...,Nk in G such that G can be embedded into a graph H in GG such that for every edge e in H which is not an edge in G, there exists an i such that both endpoints of e are in Ni. For the class TH of threshold graphs we show that TH-width is NP-complete and we present fixed-parameter algorithms. We also show that for each k, graphs of TH-width at most k are characterized by a finite collection of forbidden induced subgraphs.
Keywords
Cite
@article{arxiv.1210.8365,
title = {On the threshold-width of graphs},
author = {M. Chang and L. Hung and T. Kloks and S. Peng},
journal= {arXiv preprint arXiv:1210.8365},
year = {2012}
}