Chordal directed graphs are not $\chi$-bounded
Combinatorics
2022-02-03 v1
Abstract
We show that digraphs with no transitive tournament on vertices and in which every induced directed cycle has length can have arbitrarily large dichromatic number. This answers to the negative a question of Carbonero, Hompe, Moore, and Spirkl (and extends some of their results).
Cite
@article{arxiv.2202.01006,
title = {Chordal directed graphs are not $\chi$-bounded},
author = {Pierre Aboulker and Nicolas Bousquet and Rémi de Verclos},
journal= {arXiv preprint arXiv:2202.01006},
year = {2022}
}