Square of a Hamilton cycle in a random graph

Patrick Bennett, Andrzej Dudek, Alan Frieze

Published 2016-11-20Version 1

We show that the threshold for the random graph $G_{n,p}$ to contain the square of a Hamilton cycle is $p=\frac{1}{\sqrt{n}}$. This improves the previous results of K\"uhn and Osthus and also Nenadov and \v{S}kori\'c.