Hamiltonicity in randomly perturbed hypergraphs

For integers k >= 3 and 1 <= l <= k - 1, we prove that for any alpha > 0, there exist epsilon > 0 and C > 0 such that for sufficiently large n is an element of (k - l)N, the union of a k-uniform hypergraph with minimum vertex degree alpha n(k-1) and a binomial random k-uniform hypergraph G((k)) (n, p) with p >= n(-(k-l)-epsilon) for l >= 2 and p >= Cn(-(k-1)) for l = 1 on the same vertex set contains a Hamiltonian l-cycle with high probability. Our result is best possible up to the values of epsilon and C and answers a question of Krivelevich, Kwan and Sudakov. (C) 2020 Elsevier Inc. All rights reserved.