Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Density Version of the Corradi-Hajnal Theorem   For every positive integer $k$, we show that every graph of order $n$ at
least $3k$ with more than $$\max\{{2k-1\choose 2}+(2k-1)(n-(2k-1)),{3k-1\choose
2}+(n-(3k-1))\}$$ edges has $k$ vertex disjoint cycles, which is a best
possible density version of a theorem of Corr\'{a}di and Hajnal.

23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol