Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The maximum number of cliques in a graph embedded in a surface   This paper studies the following question: Given a surface $\Sigma$ and an
integer $n$, what is the maximum number of cliques in an $n$-vertex graph
embeddable in $\Sigma$? We characterise the extremal graphs for this question,
and prove that the answer is between $8(n-\omega)+2^{\omega}$ and $8n+{3/2}
2^{\omega}+o(2^{\omega})$, where $\omega$ is the maximum integer such that the
complete graph $K_\omega$ embeds in $\Sigma$. For the surfaces $\mathbb{S}_0$,
$\mathbb{S}_1$, $\mathbb{S}_2$, $\mathbb{N}_1$, $\mathbb{N}_2$, $\mathbb{N}_3$
and $\mathbb{N}_4$ we establish an exact answer.

23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org