Planar 4-critical graphs with four triangles

Oleg V. Borodin, Zdeněk Dvořák, Alexandr V. Kostochka, Bernard Lidický, Matthew Yancey

Research output: Contribution to journalArticlepeer-review


By the Grünbaum-Aksenov Theorem (extending Grötzsch'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.

Original languageEnglish (US)
Pages (from-to)138-151
Number of pages14
JournalEuropean Journal of Combinatorics
StatePublished - Oct 2014

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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