  We show that the total variation mixing time of the simple random walk on the
giant component of supercritical Erdos-Renyi graphs is log^2 n. This statement
was only recently proved, independently, by Fountoulakis and Reed. Our proof
follows from a structure result for these graphs which is interesting in its
own right. We show that these graphs are "decorated expanders" - an expander
glued to graphs whose size has constant expectation and exponential tail, and
such that each vertex in the expander is glued to no more than a constant
number of decorations.
