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arXiv · 2602.08736

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

Guillaume Aubian·Luis Kuffner
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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.

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Guillaume Aubian, Luis Kuffner. 2026-02-09. (Claw, C_3)-free digraphs with unbounded dichromatic number. https://arxiv.org/abs/2602.08736

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