Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of the Erd\H{o}s-Simonovits conjecture on walks   Let $G^n$ be a graph on $n$ vertices and let $w_k(G^n)$ denote the number of
walks of length $k$ in $G^n$ divided by $n$. Erd\H{o}s and Simonovits
conjectured that $w_k(G^n)^t \geq w_t(G^n)^k$ when $k\geq t$ and both $t$ and
$k$ are odd. We prove this conjecture.

30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol