The acyclic dichromatic number of an oriented graph is the minimum size of a vertex-partition such that the digraphs induced by any single part are acyclic, and the oriented bipartite graphs between any two parts are acyclic too. We characterize the subtournaments that must appear in every tournament with sufficiently large acyclic dichromatic number, thereby confirming a conjecture of Bang-Jensen, Picasarri-Arrieta, and Yeo and prove that acyclic dichromatic number satisfies a local to global property.

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