Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cycles of given size in a dense graph   We generalise a result of Corr\'{a}di and Hajnal and show that every graph
with average degree at least $\tfrac{4}{3}kr$ contains $k$ vertex disjoint
cycles, each of order at least $r$, as long as $k \geq 6$. This bound is sharp
when $r=3$.

28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn