Sub-exponentially many 3-colorings of triangle-free planar graphs
Combinatorics
2011-03-31 v2
Abstract
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.
Cite
@article{arxiv.1007.1430,
title = {Sub-exponentially many 3-colorings of triangle-free planar graphs},
author = {Arash Asadi and Zdenek Dvorak and Luke Postle and Robin Thomas},
journal= {arXiv preprint arXiv:1007.1430},
year = {2011}
}
Comments
10 pages. Simplified proof. Added a coauthor