Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Powers of tight Hamilton cycles in randomly perturbed hypergraphs   For $k\ge 2$ and $r\ge 1$ such that $k+r\ge 4$, we prove that, for any
$\alpha>0$, there exists $\epsilon>0$ such that the union of an $n$-vertex
$k$-graph with minimum codegree
$\left(1-\binom{k+r-2}{k-1}^{-1}+\alpha\right)n$ and a binomial random
$k$-graph $\mathbb{G}^{(k)}(n,p)$ with $p\ge
n^{-\binom{k+r-2}{k-1}^{-1}-\epsilon}$ on the same vertex set contains the
$r^{\text{th}}$ power of a tight Hamilton cycle with high probability. This
result for $r=1$ was first proved by McDowell and Mycroft.

35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg