Density of 5/2-critical graphs
Combinatorics
2014-11-26 v1
Abstract
A graph G is 5/2-critical if G has no circular 5/2-coloring (or equivalently, homomorphism to C_5), but every proper subgraph of G has one. We prove that every 5/2-critical graph on n>=4 vertices has at least (5n-2)/4 edges, and list all 5/2-critical graphs achieving this bound. This implies that every planar or projective-planar graph of girth at least 10 is 5/2-colorable.
Keywords
Cite
@article{arxiv.1411.6668,
title = {Density of 5/2-critical graphs},
author = {Zdenek Dvorak and Luke Postle},
journal= {arXiv preprint arXiv:1411.6668},
year = {2014}
}
Comments
26 pages, 3 figures