  Random graph alignment refers to recovering the underlying vertex
correspondence between two random graphs with correlated edges. This can be
viewed as an average-case and noisy version of the well-known graph isomorphism
problem. For the correlated Erd\"os-R\'enyi model, we prove an impossibility
result for partial recovery in the sparse regime, with constant average degree
and correlation, as well as a general bound on the maximal reachable overlap.
Our bound is tight in the noiseless case (the graph isomorphism problem) and we
conjecture that it is still tight with noise. Our proof technique relies on a
careful application of the probabilistic method to build automorphisms between
tree components of a subcritical Erd\"os-R\'enyi graph.
