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Let $f(r, \\Delta)$ be the smallest integer $k$ such that each $r$-uniform hypergraph of maximum vertex degree $\\Delta$ has a conflict-free coloring with at most $k$ colors. As shown by Tardos and Pach, similarly to a classical Brooks' type theorem for hypergraphs, $f(r, \\Delta)\\leq \\Delta+1$. 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