Hamiltonicity in randomly perturbed hypergraphs

Abstract For integers k ≥ 3 and 1 ≤ l ≤ k − 1 , we prove that for any α > 0 , there exist ϵ > 0 and C > 0 such that for sufficiently large n ∈ ( k − l ) N , the union of a k-uniform hypergraph with minimum vertex degree α n k − 1 and a binomial random k-uniform hypergraph G ( k ) ( n , p ) with p ≥ n − ( k − l ) − ϵ for l ≥ 2 and p ≥ C n − ( 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 ϵ and C and answers a question of Krivelevich, Kwan and Sudakov.