(Claw, C3)-free digraphs with unbounded dichromatic number
Abstract
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.
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