Almost every $n$-vertex graph is determined by its $3 \log_2{n}$-vertex subgraphs

Abstract

The paper shows that almost every $n$-vertex graph is such that the multiset of its induced subgraphs on $3 \log_2{n}$ vertices is sufficient to determine it up to isomorphism. Therefore, for checking the isomorphism of a pair of $n$-vertex graphs, almost surely the multiset of their $3 \log_2{n}$-vertex subgraphs is sufficient .