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A majority coloring of a digraph with colors is an assignment such that for every we have for at most half of all out-neighbors . A digraph is majority -choosable if for any assignment of lists of colors of size to the vertices, there is a majority coloring of from these lists. We prove that if is a 1-planar graph without a 4-cycle, then is majority 3-choosable. And we also prove that every NIC-planar digraph is majority 3-choosable.
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