Square of Hamilton cycle in a random graph

Andrzej Dudek; Alan Frieze

Square of Hamilton cycle in a random graph

Combinatorics 2016-09-20 v3

Authors: Andrzej Dudek , Alan Frieze

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 K\"uhn and Osthus and also Nenadov and \v{S}kori\'c.

Keywords

hamilton cycles graph cycles random graphs

Cite

@article{arxiv.1606.07833,
  title  = {Square of Hamilton cycle in a random graph},
  author = {Andrzej Dudek and Alan Frieze},
  journal= {arXiv preprint arXiv:1606.07833},
  year   = {2016}
}

Comments

This paper has been withdrawn due to an error in the second moment calculations.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

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