Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the clique number of the square of a line graph and its relation to
  Ore-degree   In 1985, Erd\H{o}s and Ne\v{s}et\v{r}il conjectured that the square of the
line graph of a graph $G$, that is $L(G)^2$, can be colored with
$\frac{5}{4}\Delta(G)^2$ colors. This conjecture implies the weaker conjecture
that the clique number of such a graph, that is $\omega(L(G)^2)$, is at most
$\frac{5}{4}\Delta(G)^2$. In 2015, \'Sleszy\'nska-Nowak proved that
$\omega(L(G)^2)\le \frac{3}{2}\Delta(G)^2$. In this paper, we prove that
$\omega(L(G)^2)\le \frac{4}{3}\Delta(G)^2$. This theorem follows from our
stronger result that $\omega(L(G)^2)\le \frac{\sigma(G)^2}{3}$ where $\sigma(G)
:= \max_{uv\in E(G)} d(u) + d(v)$, is the Ore-degree of the graph $G$.

24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat