Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tur\'an number of disjoint triangles in 4-partite graphs   Let $k\ge 2$ and $n_1\ge n_2\ge n_3\ge n_4$ be integers such that $n_4$ is
sufficiently larger than $k$. We determine the maximum number of edges of a
4-partite graph with parts of sizes $n_1,\dots, n_4$ that does not contain $k$
vertex-disjoint triangles. For any $r> t\ge 3$, we give a conjecture on the
maximum number of edges of an $r$-partite graph that does not contain $k$
vertex-disjoint cliques $K_t$.

31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin