Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Avoiding long Berge cycles   Let $n\geq k\geq r+3$ and $\mathcal H$ be an $n$-vertex $r$-uniform
hypergraph. We show that if $|\mathcal H|> \frac{n-1}{k-2}\binom{k-1}{r}$ then
$\mathcal H$ contains a Berge cycle of length at least $k$. This bound is tight
when $k-2$ divides $n-1$. We also show that the bound is attained only for
connected $r$-uniform hypergraphs in which every block is the complete
hypergraph $K^{(r)}_{k-1}$. We conjecture that our bound also holds in the case
$k=r+2$, but the case of short cycles, $k\leq r+1$, is different.

8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th