On the Minimum Edge-Density of 4-Critical Graphs of Girth Five
Combinatorics
2014-09-19 v1
Abstract
We prove that if G is a 4-critical graph of girth at least five then |E(G)|>=(5|V(G)|+2)/3. As a corollary, graphs of girth at least five embeddable in the Klein bottle or torus are 3-colorable. These are results of Thomas and Walls, and Thomassen respectively. The proof uses the new potential technique developed by Kostochka and Yancey who proved that 4-critical graphs satisfy: |E(G)|>=(5|V(G)|-2)/3.
Cite
@article{arxiv.1409.5295,
title = {On the Minimum Edge-Density of 4-Critical Graphs of Girth Five},
author = {Chun-Hung Liu and Luke Postle},
journal= {arXiv preprint arXiv:1409.5295},
year = {2014}
}
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17 pages