On the number of Hamilton cycles in sparse random graphs
Combinatorics
2012-07-12 v1 Probability
Abstract
We prove that the number of Hamilton cycles in the random graph G(n,p) is n!p^n(1+o(1))^n a.a.s., provided that p\geq (ln n+ln ln n+\omega(1))/n. Furthermore, we prove the hitting-time version of this statement, showing that in the random graph process, the edge that creates a graph of minimum degree 2 creates (ln n/e)^n(1+o(1))^n Hamilton cycles a.a.s.
Cite
@article{arxiv.1207.2748,
title = {On the number of Hamilton cycles in sparse random graphs},
author = {R. Glebov and M. Krivelevich},
journal= {arXiv preprint arXiv:1207.2748},
year = {2012}
}
Comments
18 pages