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Planar 4-critical graphs with four triangles
Published 6 Jun 2013 in math.CO and cs.DM | (1306.1477v1)
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.
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