Sub-Exponentially Many 3-Colorings of Triangle-Free Planar Graphs

Arash Asadi, Luke Postle, Robin Thomas
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="" style="color: black;">Electronic Notes in Discrete Mathematics</a> </i> &nbsp;
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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1016/j.endm.2009.07.014</a> <a target="_blank" rel="external noopener" href="">fatcat:opdqk3sqvvhxrnz6yysxak2yrq</a> </span>
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