Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chromatic numbers of Kneser-type graphs   Let $G(n, r, s)$ be a graph whose vertices are all $r$-element subsets of an
$n$-element set, in which two vertices are adjacent if they intersect in
exactly $s$ elements. In this paper we study chromatic numbers of $G(n, r, s)$
with $r, s$ being fixed constants and $n$ tending to infinity. Using a recent
result of Keevash on existence of designs we deduce an inequality $\chi(G(n, r,
s)) \le (1+o(1))n^{r-s} \frac{(r-s-1)!}{(2r-2s-1)!}$ for $r > s$ with $r, s$
fixed constants. This inequality gives sharp upper bounds for $r \le 2s+1$.
Also we develop an elementary approach to this problem and prove that
$\chi(G(n, 4, 2)) \sim \frac{n^2}{6}$ without use of Keevash's results.
  Some bounds on the list chromatic number of $G(n, r, s)$ are also obtained.

29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org