Powers of tight Hamilton cycles in randomly perturbed hypergraphs. Issue 4 (30th July 2019) - Bedenknecht, Wiebke; Han, Jie; Kohayakawa, Yoshiharu; Mota, Guilherme O.
Abstract : For k  ≥ 2 and r  ≥ 1 such that k  +  r  ≥ 4, we prove that, for any α  > 0, there exists ε  > 0 such that the union of an n ‐vertex k ‐graph with minimum codegree 1 − k + r − 2 k − 1 − 1 + α n and a binomial random k ‐graph G ( k ) ( n, p ) with p ≥ n − k + r − 2 k − 1 − 1 − ε on the same vertex set contains the r th power of a tight Hamilton cycle with high probability. This result for r  = 1 was first proved by McDowell and Mycroft.