Solution to a problem of Gr\"unbaum on the edge density of $4$-critical planar graphs

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arxiv 2311.03132 v1 pith:FJI5RJM6 submitted 2023-11-06 math.CO

Zdeněk Dvořák , Carl Feghali This is my paper · ORCID

classification math.CO

keywords criticalgraphsplanarunbaumansweringdensityedgelimsup

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abstract

We show that $\limsup |E(G)|/|V(G)| = 2.5$ over all $4$-critical planar graphs $G$, answering a question of Gr\"unbaum from 1988.