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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

Dichromatic number of chordal graphs

Résumé

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.

Dates et versions

hal-04379896 , version 1 (08-01-2024)

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Stéphane Bessy, Frédéric Havet, Lucas Picasarri-Arrieta. Dichromatic number of chordal graphs. 2023. ⟨hal-04379896⟩
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