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Acyclic Dicolourings of Oriented Graphs: Paths, Random Tournaments, and Critical Orders
An acyclic dicolouring of an oriented graph is a vertex partition in which every colour class and every bipartite subdigraph induced by two classes is acyclic. We first prove the Gallai--Roy-type bound $\vecχ_a(D)\leq L(D)$, where $L(D)$ is the maximum order of a directed path. Let $r=\log_2(8/7)$.
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