Eran Ofek

Let $d \geq d_0$ be a sufficiently large constant. A $(n,d,c

\sqrt{d})$ graph $G$ is a $d$ regular graph over $n$ vertices whose

second largest eigenvalue (in absolute value) is at most $c

\sqrt{d}$. For any $0 < p < 1, ~G_p$ is the graph induced by

retaining each edge ...
more >>>