{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T20:10:09Z","timestamp":1751659809593,"version":"3.41.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The dichromatic number of a digraph $D$ is the smallest $k$ such that $D$ can be partitioned into $k$ acyclic subdigraphs, and the dichromatic number of an undirected graph is the maximum dichromatic number over all its orientations. Extending a well-known result of Lov\u00e1sz, we show that the dichromatic number of the Kneser graph $KG(n,k)$ is $\\Theta(n-2k+2)$ and that the dichromatic number of the Borsuk graph $BG(n+1,a)$ is $n+2$ if $a$ is large enough. We then study the list version of the dichromatic number. We show that, for any $\\varepsilon&gt;0$ and $2\\leq k\\leq n^{\\frac{1}{2}-\\varepsilon}$, the list dichromatic number of $KG(n,k)$ is $\\Theta(n\\ln n)$. This extends a recent result of Bulankina and Kupavskii on the list chromatic number of $KG(n,k)$, where the same behaviour was observed. We also show that for any $\\rho&gt;3$, $r\\geq 2$ and $m\\geq\\max\\{\\ln^{\\rho}r,2\\}$, the list dichromatic number of the complete $r$-partite graph with $m$ vertices in each part is $\\Theta(r\\ln m)$, extending a classical result of Alon. Finally, we give a directed analogue of Sabidussi's theorem on the chromatic number of graph products.<\/jats:p>","DOI":"10.37236\/12315","type":"journal-article","created":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T19:54:59Z","timestamp":1751658899000},"source":"Crossref","is-referenced-by-count":0,"title":["Colouring Complete Multipartite and Kneser-Type Digraphs"],"prefix":"10.37236","volume":"32","author":[{"given":"Ararat","family":"Harutyunyan","sequence":"first","affiliation":[]},{"given":"Gil","family":"Puig i Surroca","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2025,7,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i3p1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i3p1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T19:54:59Z","timestamp":1751658899000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i3p1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,4]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/12315","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,4]]}}}