Factors in randomly perturbed hypergraphs

Abstract

AbstractWe 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 to ensure an F‐factor with high probability, for any F that belongs to a certain class of k‐graphs, which includes, for example, all k‐partite k‐graphs, 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).