Colouring quadrangulations of projective spaces
Combinatorics
2015-05-07 v2
Abstract
A graph embedded in a surface with all faces of size 4 is known as a quadrangulation. We extend the definition of quadrangulation to higher dimensions, and prove that any graph G which embeds as a quadrangulation in the real projective space P^n has chromatic number n+2 or higher, unless G is bipartite. For n=2 this was proved by Youngs [J. Graph Theory 21 (1996), 219-227]. The family of quadrangulations of projective spaces includes all complete graphs, all Mycielski graphs, and certain graphs homomorphic to Schrijver graphs. As a corollary, we obtain a new proof of the Lovasz-Kneser theorem.
Keywords
Cite
@article{arxiv.1310.5875,
title = {Colouring quadrangulations of projective spaces},
author = {Tomáš Kaiser and Matěj Stehlík},
journal= {arXiv preprint arXiv:1310.5875},
year = {2015}
}