(Claw, C_3)-free digraphs with unbounded dichromatic number

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Guillaume Aubian, Luis Kuffner
DOI: 10.48550/arxiv.2602.08736
Cited by: 0

Abstract

We construct orientations of rook graphs (whose underlying graphs are claw-free) that contain no directed $C_3$ but have unbounded dichromatic number. This disproves a conjecture of Aboulker, Charbit and Naserasr and improves a result of Carbonero, Koerts, Moore and Spirkl.

Fields of Study & Subjects

Advanced Graph Theory Research Limits and Structures in Graph Theory Advanced Topology and Set Theory

Publication details

Journal / source
arXiv (Cornell University)
Publication date
9 February 2026
Language
EN
Document type
Preprint