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- W4285689035 abstract "The digirth of a digraph is the length of a shortest directed cycle. The dichromatic number $vec{chi}(D)$ of a digraph $D$ is the smallest size of a partition of the vertex-set into subsets inducing acyclic subgraphs. A conjecture by Harutyunyan and Mohar states that $vec{chi}(D) le leftlceilfrac{Delta}{4}rightrceil+1$ for every digraph $D$ of digirth at least $3$ and maximum degree $Delta$. The best known partial result by Golowich shows that $vec{chi}(D) le frac{2}{5}Delta+O(1)$. In this short note we prove for every $g ge 2$ that if $D$ is a digraph of digirth at least $2g-1$ and maximum degree $Delta$, then $vec{chi}(D) le (frac{1}{3}+frac{1}{3g}) Delta + O_g(1)$. This improves the bound of Golowich for digraphs without directed cycles of length at most $10$." @default.
- W4285689035 created "2022-07-18" @default.
- W4285689035 creator A5010407419 @default.
- W4285689035 date "2020-04-04" @default.
- W4285689035 modified "2023-09-26" @default.
- W4285689035 title "A Note on Coloring Digraphs of Large Girth" @default.
- W4285689035 doi "https://doi.org/10.48550/arxiv.2004.01925" @default.
- W4285689035 hasPublicationYear "2020" @default.
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