On the number of Hamilton cycles in pseudo-random graphs
Combinatorics
2012-01-10 v2
Abstract
We prove that if G is an (n,d,lambda)-graph (a d-regular graph on n vertices, all of whose non-trivial eigenvalues are at most lambda) and the following conditions are satisfied: 1. d/lambda >= (log n)^{1+epsilon} for some constant epsilon>0; 2.log d * lod (d/lambda) >> log n, then the number of Hamilton cycles in G is n!(d/n)^n(1+o(1))^n.
Cite
@article{arxiv.1111.6261,
title = {On the number of Hamilton cycles in pseudo-random graphs},
author = {Michael Krivelevich},
journal= {arXiv preprint arXiv:1111.6261},
year = {2012}
}