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arXiv · 2309.17385

Dichromatic number of chordal graphs

Stéphane Bessy·Frédéric Havet·Lucas Picasarri-Arrieta
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Abstract

The dichromatic number of a digraph is the minimum integer $k$ such that it admits a $k$-dicolouring, i.e. a partition of its vertices into $k$ acyclic subdigraphs. We say that a digraph $D$ is a super-orientation of an undirected graph $G$ if $G$ is the underlying graph of $D$. If $D$ does not contain any pair of symmetric arcs, we just say that $D$ is an orientation of $G$. In this work, we give both lower and upper bounds on the dichromatic number of super-orientations of chordal graphs. We also show a family of orientations of cographs for which the dichromatic number is equal to the clique number of the underlying graph.

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Stéphane Bessy, Frédéric Havet, Lucas Picasarri-Arrieta. 2025-02-26. Dichromatic number of chordal graphs. https://arxiv.org/abs/2309.17385

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