On Uni Chord Free Graphs
Discrete Mathematics
2014-10-27 v3
Abstract
A graph is unichord free if it does not contain a cycle with exactly one chord as its subgraph. In [3], it is shown that a graph is unichord free if and only if every minimal vertex separator is a stable set. In this paper, we first show that such a graph can be recognized in polynomial time. Further, we show that the chromatic number of unichord free graphs is one of (2,3, \omega(G)). We also present a polynomial-time algorithm to produce a coloring with \omega(G) colors.
Cite
@article{arxiv.1311.1928,
title = {On Uni Chord Free Graphs},
author = {Mahati Kumar and S. Manasvini and N. Sadagopan and Adithya Seshadri},
journal= {arXiv preprint arXiv:1311.1928},
year = {2014}
}
Comments
This paper has been withdrawn due to a bug in the algorithm