Almost Every n-Vertex Graph is Determined by Its 3log2n-Vertex Subgraphs

Abstract

This paper proves that almost every [Formula: see text]-vertex graph has the property that the multiset of its induced subgraphs on [Formula: see text] vertices is sufficient to determine it up to isomorphism. That is, the probability that there exists two [Formula: see text]-vertex graphs with the same multiset of [Formula: see text]-vertex induced subgraphs goes to zero as [Formula: see text] goes to infinity.