We construct orientations of rook graphs (whose underlying graphs are claw-free) that contain no directed C3 but have unbounded dichromatic number. This disproves a conjecture of Aboulker, Charbit and Naserasr and improves a result of Carbonero, Koerts, Moore and Spirkl.
Cite
@article{arxiv.2602.08736,
title = {(Claw, C_3)-free digraphs with unbounded dichromatic number},
author = {Guillaume Aubian and Luis Kuffner},
journal= {arXiv preprint arXiv:2602.08736},
year = {2026}
}