Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chromatic thresholds in dense random graphs   The chromatic threshold $\delta_\chi(H,p)$ of a graph $H$ with respect to the
random graph $G(n,p)$ is the infimum over $d > 0$ such that the following holds
with high probability: the family of $H$-free graphs $G \subset G(n,p)$ with
minimum degree $\delta(G) \ge dpn$ has bounded chromatic number. The study of
the parameter $\delta_\chi(H) := \delta_\chi(H,1)$ was initiated in 1973 by
Erd\H{o}s and Simonovits, and was recently determined for all graphs $H$. In
this paper we show that $\delta_\chi(H,p) = \delta_\chi(H)$ for all fixed $p
\in (0,1)$, but that typically $\delta_\chi(H,p) \ne \delta_\chi(H)$ if $p =
o(1)$. We also make significant progress towards determining $\delta_\chi(H,p)$
for all graphs $H$ in the range $p = n^{-o(1)}$. In sparser random graphs the
problem is somewhat more complicated, and is studied in a separate paper.

17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg