Square of Hamilton cycle in a random graph

Andrzej Dudek, Alan Frieze

Published 2016-06-24Version 1

We show that if $\beta>0$ is constant and $p\geq \sqrt{\frac{\beta\log n}{n}}$ then w.h.p. the random graph $G_{n,p}$ contains the square of a Hamilton cycle. This improves the previous results of K\"uhn and Osthus and also Nenadov and \v{S}kori\'c.