Subgraph isomorphism problem

In complexity theory, Subgraph-Isomorphism is a decision problem that is known to be NP-complete. The formal description of the decision problem is as follows.

Subgraph-Isomorphism(G1, G2) Input: Two graphs G1 and G2. Question: Is G1 isomorphic to a subgraph of G2?

Sometimes the name subgraph matching is also used for the same problem. This name puts emphasis on finding such a subgraph as opposed to the bare decision problem.

Subgraph isomorphism is a generalization of the potentially easier graph isomorphism problem; if the graph isomorphism problem is NP-complete, the polynomial hierarchy collapses, so it is suspected not to be.

Application areas
In the area of cheminformatics often the term substructure search is used. Typically a query structure is defined as SMARTS, a SMILES extension.

Also of main importance to graph grammars.