Square of Hamilton cycle in a random graph

Abstract

We show that $p=\sqrt{\frac{e}{n}}$ is a sharp threshold for the random graph $G_{n,p}$ to contain the square of a Hamilton cycle. This improves the previous results of Kühn and Osthus and also Nenadov and Škorić.

This paper has been withdrawn due to an error in the second moment calculations. We thank Asaf Ferber and Matthew Kwan for drawing our attention to this issue