Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factors in randomly perturbed hypergraphs   We determine, up to a multiplicative constant, the optimal number of random
edges that need to be added to a $k$-graph $H$ with minimum vertex degree
$\Omega(n^{k-1})$ to ensure an $F$-factor with high probability, for any $F$
that belongs to a certain class $\mathcal{F}$ of $k$-graphs, which includes,
e.g., all $k$-partite $k$-graphs, $K_4^{(3)-}$ and the Fano plane. In
particular, taking $F$ to be a single edge, this settles a problem of
Krivelevich, Kwan and Sudakov [Combin. Probab. Comput. 25 (2016), 909--927]. We
also address the case in which the host graph $H$ is not dense, indicating that
starting from certain such $H$ is essentially the same as starting from an
empty graph (namely, the purely random model).

26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int