The Graph Clustering Problem has a Perfect Zero-Knowledge Proof

The Graph Clustering Problem is parameterized by a sequence of positive integers, m 1 ; :::; m t. The input is a sequence of P t i=1 m i graphs, and the question is whether the equivalence classes under the graph isomorphism relation have sizes which match the sequence of parameters. In this note we show that this problem has a (perfect) zero-knowledge interactive proof system.