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arXiv · 1805.01948

Coloring even-hole-free graphs with no star cutset

Ngoc Khang Le
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Abstract

A \emph{hole} is a chordless cycle of length at least $4$. A graph is \emph{even-hole-free} if it does not contain any hole of even length as an induced subgraph. In this paper, we study the class of even-hole-free graphs with no star cutset. We give the optimal upper bound for its chromatic number in terms of clique number and a polynomial-time algorithm to color any graph in this class. The latter is, in fact, a direct consequence of our proof that this class has bounded rank-width.

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Ngoc Khang Le. 2018-05-04. Coloring even-hole-free graphs with no star cutset. https://arxiv.org/abs/1805.01948

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