Borel directed graphs of bounded degree admit mu-measurable and Baire-measurable d-dicolorings unless containing the complete symmetric digraph on d+1 vertices, plus a definable Gallai theorem for list dicolorings.
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Measurable Brooks's Theorem for Directed Graphs
Borel directed graphs of bounded degree admit mu-measurable and Baire-measurable d-dicolorings unless containing the complete symmetric digraph on d+1 vertices, plus a definable Gallai theorem for list dicolorings.