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Thomassen conjectured that every triangle-free planar graph on n vertices has exponentially many 3-colorings, and proved that it has at least 2^[n^(1/12)/20000] distinct 3-colorings. We show that it has at least 2^sqrt(n/362) distinct 3-colorings.arXiv:1007.1430v2 fatcat:ljahmr6smrc4tc4bbribvtqksa