English

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.

Keywords

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This paper has been withdrawn due to a bug in the algorithm

R2 v1 2026-06-22T02:03:37.163Z