We denote the fingerprint of a structure s by FP(s). We can use a fingerprint to heuristically speed up substructure search, if there is an easily verifiable property for the fingerprints of graphs G and G that must hold if G is a subgraph of G. There are a number of binary fingerprints with the property that if G is a subgraph of G, then FP(G ) ⊆ FP(G). This property holds for various common fingerprints, e.g. path fingerprints, tree fingerprints, or some configurations of the CSFP from Bellman and Rarey. 11 Any of these can be used to accelerate substructure search.