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

• Record Type: Journal Article
• Authors: Bedenknecht, Wiebke; Han, Jie; Kohayakawa, Yoshiharu; Mota, Guilherme O.
• Is Part Of: Random structures & algorithms. Volume 55:Issue 4(2019)
• Page Start: 795
• Page End: 807
• Publication Date: 2019-07-30
• Subjects: perturbed hypergraphs -- powers of Hamilton cycles -- random hypergraphs; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20885
• Languages: English
• ISSNs: 1042-9832

Abstract

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.