Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On powers of tight Hamilton cycles in randomly perturbed hypergraphs   We show that for $k \geq 3$, $r\geq 2$ and $\alpha> 0$, there exists
$\varepsilon > 0$ such that if $p=p(n)\geq
n^{-{\binom{k+r-2}{k-1}}^{-1}-\varepsilon}$ and $H$ is a $k$-uniform hypergraph
on $n$ vertices with minimum codegree at least $\alpha n$, then asymptotically
almost surely the union $H\cup G^{(k)}(n,p)$ contains the $r^{th}$ power of a
tight Hamilton cycle. The bound on $p$ is optimal up to the value of
$\varepsilon$ and this answers a question of Bedenknecht, Han, Kohayakawa and
Mota.

10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph