On Posa's conjecture for random graphs
Combinatorics
2012-07-31 v2
Abstract
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}.
Cite
@article{arxiv.1203.6310,
title = {On Posa's conjecture for random graphs},
author = {Daniela Kühn and Deryk Osthus},
journal= {arXiv preprint arXiv:1203.6310},
year = {2012}
}
Comments
includes minor revisions, accepted for publication in SIAM Journal Discrete Mathematics