Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The chromatic number of a two families of generalized Kneser graphs
  related to finite generalized quadrangles and finite projective 3-spaces   Let $\Gamma$ be the graph whose vertices are the chambers of the finite
projective space $PG(3,q)$ with two vertices being adjacent when the
corresponding chambers are in general position. It is known that the
independence number of this graph is $(q^2+q+1)(q+1)^2$. For $q\ge 43$ we
determine the largest independent set of $\Gamma$ and show that every maximal
independent set that is not a largest one has at most constant times $q^3$
elements. For $q\ge 47$, this information is then used to show that $\Gamma$
has chromatic number $q^2+q$. Furthermore, for many families of generalized
quadrangles we prove similar results for the graph that is built in the same
way on the chambers of the generalized quadrangle.

11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin