Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enhancing the Erd\H{o}s-Lov\'asz Tihany Conjecture for line graphs of
  multigraphs   In this paper, we prove an enhanced version of the Erd\H{o}s-Lov\'asz Tihany
Conjecture for line graphs of multigraphs. That is, for every graph $G$ whose
chromatic number $\chi(G)$ is more than its clique number $\omega(G)$ and for
nonnegative integer $\ell$, any two integers $s,t \geq 3.5\ell+2$ with $s+t =
\chi(G)+1$, there is a partition $(S,T)$ of the vertex set $V(G)$ such that
$\chi(G[S])\geq s$ and $\chi(G[T])\geq t+\ell$. In particular, when $\ell=1$,
we can obtain the same result just for any $s,t\geq4$. The Erd\H{o}s-Lov\'asz
Tihany conjecture is a special case when $\ell=0$.

28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph