Sub-exponentially many 3-colorings of triangle-free planar graphs
Arash Asadi, Zdenĕk Dvořák, Luke Postle, Robin B. Thomas · arXiv (Cornell University) · 2010
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.