  We consider the problem of perfectly recovering the vertex correspondence
between two correlated Erd\H{o}s-R\'enyi (ER) graphs on the same vertex set.
The correspondence between the vertices can be obscured by randomly permuting
the vertex labels of one of the graphs. We determine the information-theoretic
threshold for exact recovery, i.e. the conditions under which the entire vertex
correspondence can be correctly recovered given unbounded computational
resources.
