@article {IOPORT.06045649, author = {Krivelevich, Michael}, title = {On the number of Hamilton cycles in pseudo-random graphs.}, year = {2012}, journal = {The Electronic Journal of Combinatorics [electronic only]}, volume = {19}, number = {1}, issn = {1077-8926}, pages = {Research Paper P25, 14 p., electronic only}, publisher = {Prof. Andr\'e K\"undgen, Deptartment of Mathematics, California State University San Marcos, San Marcos, CA}, abstract = {Summary: 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: { indent=6mm \item{1)}$\frac{d}{\lambda}\ge (\log n)^{1+\epsilon}$ for some constant $\epsilon>0$ and \item{2)}$\log d\cdot \log\frac{d}{\lambda}\gg \log n$, then the number of Hamilton cycles in $G$ is $n!\left(\frac{d}{n}\right)^n(1+o(1))^n$. }}, identifier = {06045649}, }