English

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.

Keywords

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