Planar 4-critical graphs with four triangles
Combinatorics
2016-12-16 v1 Discrete Mathematics
Abstract
By the Grunbaum-Aksenov Theorem (extending Grotzsch's Theorem) every planar graph with at most three triangles is 3-colorable. However, there are infinitely many planar 4-critical graphs with exactly four triangles. We describe all such graphs. This answers a question of Erdos from 1990.
Cite
@article{arxiv.1306.1477,
title = {Planar 4-critical graphs with four triangles},
author = {Oleg V. Borodin and Zdeněk Dvořák and Alexandr V. Kostochka and Bernard Lidický and Matthew Yancey},
journal= {arXiv preprint arXiv:1306.1477},
year = {2016}
}
Comments
20 pages, 7 figures