English

Coloring even-hole-free graphs with no star cutset

Discrete Mathematics 2018-06-08 v1 Combinatorics

Abstract

A \emph{hole} is a chordless cycle of length at least 44. 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.

Keywords

Cite

@article{arxiv.1805.01948,
  title  = {Coloring even-hole-free graphs with no star cutset},
  author = {Ngoc Khang Le},
  journal= {arXiv preprint arXiv:1805.01948},
  year   = {2018}
}
R2 v1 2026-06-23T01:45:41.991Z