Dichromatic number of chordal graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915172903288832 |
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| author | Bessy, Stéphane Havet, Frédéric Picasarri-Arrieta, Lucas |
| author_facet | Bessy, Stéphane Havet, Frédéric Picasarri-Arrieta, Lucas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_17385 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dichromatic number of chordal graphs Bessy, Stéphane Havet, Frédéric Picasarri-Arrieta, Lucas Combinatorics Discrete Mathematics 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. |
| title | Dichromatic number of chordal graphs |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2309.17385 |