In the paper "Sharp thresholds for higher powers of Hamilton cycles in random graphs" Leon Schiller, Matija Pasch, Kalina Petrova and Tamas Makai prove that there is a sharp threshold for the existence of the k-th power of a Hamilton cycle in a Erdős–Rényi random graph G(n,p) at p = (e/n)^{1/k}, for all k >= 4. Our proof employs the second moment method and can be seen as an adaptation of the method introduced by Riordan (“Spanning Subgraphs of Random Graphs”, Combinatorics, Probability and Computing, 2000) obtained by treating sparse and dense subgraphs of the considered spanning subgraph separately. This paper will be presented at EUROCOMB, August 25th to August 30th at Hungarian Academy of Sciences, Budapest.
