*Yulin Chang (Shandong University)
Jie Han (University of Rhode Island)
Yoshiharu Kohayakawa (Universidade de Sao Paulo)
Patrick Morris (Freie Universitat Berlin and Berlin Mathematical School)
Guilherme Oliveira Mota (Universidade de Sao Paulo)

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).
This is a joint work with Jie Han, Yoshiharu Kohayakawa, Patrick Morris and Guilherme Oliveira Mota.