English

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

Combinatorics 2023-11-07 v1

Abstract

We show that lim supE(G)/V(G)=2.5\limsup |E(G)|/|V(G)| = 2.5 over all 44-critical planar graphs GG, answering a question of Gr\"unbaum from 1988.

Keywords

Cite

@article{arxiv.2311.03132,
  title  = {Solution to a problem of Gr\"unbaum on the edge density of $4$-critical planar graphs},
  author = {Zdeněk Dvořák and Carl Feghali},
  journal= {arXiv preprint arXiv:2311.03132},
  year   = {2023}
}

Comments

14 pages, 7 figures