Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Colouring quadrangulations of projective spaces   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.

25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int