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Sub-Exponentially Many 3-Colorings of Triangle-Free Planar Graphs
<span title="">2009</span>
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<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fhi2xwpnh5gmlgof2idwu5wlgq" style="color: black;">Electronic Notes in Discrete Mathematics</a>
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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 √ n/362 distinct 3-colorings.
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