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arXiv · 1311.1928

On Uni Chord Free Graphs

Mahati Kumar·S. Manasvini·N. Sadagopan·Adithya Seshadri
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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, ω(G)). We also present a polynomial-time algorithm to produce a coloring with ω(G) colors.

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Mahati Kumar, S. Manasvini, N. Sadagopan, Adithya Seshadri. 2014-10-24. On Uni Chord Free Graphs. https://arxiv.org/abs/1311.1928

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