On powers of tight Hamilton cycles in randomly perturbed hypergraphs

Abstract

AbstractFor integers and , we show that for every , there exists such that the union of ‐uniform hypergraph on vertices with minimum codegree at least and a binomial random ‐uniform hypergraph with on the same vertex set contains the power of a tight Hamilton cycle with high probability. Moreover, a construction shows that one cannot take , where is a constant. Thus the bound on is optimal up to the value of and this answers a question of Bedenknecht, Han, Kohayakawa, and Mota.