Sub-exponentially many 3-colorings of triangle-free planar graphs

Authors:
Arash Asadi;Zdenk Dvořák;Luke Postle;Robin Thomas
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA;Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Prague 1, Czech Republic;School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA;School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2013

Citing 7
Cited 0

Gro¨tzsch's 3-color theorem and its counterparts for the torus and the projective plane

Journal of Combinatorial Theory Series B
3-list-coloring planar graphs of girth 5

Journal of Combinatorial Theory Series B
A short list color proof of Grötzsch's theorem

Journal of Combinatorial Theory Series B
Many 3-colorings of triangle-free planar graphs

Journal of Combinatorial Theory Series B
Exponentially many 5-list-colorings of planar graphs

Journal of Combinatorial Theory Series B
Coloring even-faced graphs in the torus and the Klein bottle

Combinatorica
Three-coloring triangle-free planar graphs in linear time

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

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^^^/^^^1^^^2^/^2^0^0^0^0 distinct 3-colorings. We show that it has at least 2^n^/^2^1^2 distinct 3-colorings.