A polynomial‐time approximation scheme for the maximal overlap of two independent Erdős–Rényi graphs

AbstractFor two independent Erdős–Rényi graphs , we study the maximal overlap (i.e., the number of common edges) of these two graphs over all possible vertex correspondence. We present a polynomial‐time algorithm which finds a vertex correspondence whose overlap approximates the maximal overlap up to a multiplicative factor that is arbitrarily close to 1. As a by‐product, we prove that the maximal overlap is asymptotically for with some constant .