NewEvery arXiv paper, its researchers & institutions — mapped.
paper

Planar 4-critical graphs with four triangles

arXiv:1306.1477 · doi:10.1016/j.ejc.2014.03.009

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.

20 pages, 7 figures