Factors in randomly perturbed hypergraphs. Issue 2 (20th July 2021) - Chang, Yulin; Han, Jie; Kohayakawa, Yoshiharu; Morris, Patrick; Mota, Guilherme Oliveira
Abstract: 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 Ω ( n k − 1 ) to ensure an F ‐factor with high probability, for any F that belongs to a certain class ℱ of k ‐graphs, which includes, for example, 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. 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).