Powers of tight Hamilton cycles in randomly perturbed hypergraphs. Issue 4 (30th July 2019) - Bedenknecht, Wiebke
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.