Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constraining the clustering transition for colorings of sparse random
  graphs   Let $\Omega_q$ denote the set of proper $q$-colorings of the random graph
$G_{n,m}, m=dn/2$ and let $H_q$ be the graph with vertex set $\Omega_q$ and an
edge $\{\sigma,\tau\}$ where $\sigma,\tau$ are mappings $[n]\to[q]$ iff
$h(\sigma,\tau)=1$. Here $h(\sigma,\tau)$ is the Hamming distance $|\{v\in
[n]:\sigma(v)\neq\tau(v)\}|$. We show that w.h.p. $H_q$ contains a single giant
component containing almost all colorings in $\Omega_q$ if $d$ is sufficiently
large and $q\geq \frac{cd}{\log d}$ for a constant $c>3/2$.

36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con