Tight Hamilton cycles in random hypergraphs. Issue 3 (16th October 2013) - Allen, Peter
Abstract We give an algorithmic proof for the existence of tight Hamilton cycles in a random r‐uniform hypergraph with edge probability p=n−1+ε for every ε>0. This partly answers a question of Dudek and Frieze (Random Struct Algor 42 (2013), 374–385), who used a second moment method to show that tight Hamilton cycles exist even for p=ω(n)/n (r≥3) where ω(n)→∞ arbitrary slowly, and for p=(e+o(1))/n (r≥4). The method we develop for proving our result applies to related problems as well. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 446–465, 2015