%0 Journal Article
%T On Posa's conjecture for random graphs
%A Daniela K¨¹hn
%A Deryk Osthus
%J Mathematics
%D 2012
%I arXiv
%X The famous Posa conjecture states that every graph of minimum degree at least 2n/3 contains the square of a Hamilton cycle. This has been proved for large n by Koml\'os, Sark\"ozy and Szemer\'edi. Here we prove that if p > n^{-1/2+\eps}, then asymptotically almost surely, the binomial random graph G_{n,p} contains the square of a Hamilton cycle. This provides an `approximate threshold' for the property in the sense that the result fails to hold if p< n^{-1/2}.
%U http://arxiv.org/abs/1203.6310v2