Editing Subgraph isomorphism problem (section)

{{Short description|Problem in theoretical computer science}}
[[File:Subgraph isomorphism.svg|thumb|160px|Graph <math>G</math> with a subgraph isomorphic to <math>H</math>]]
In [[theoretical computer science]], the '''subgraph isomorphism problem''' is a computational task in which two [[undirected graph|graphs]] <math>G</math> and <math>H</math> are given as input, and one must determine whether <math>G</math> contains a [[Glossary of graph theory#subgraph|subgraph]] that is [[graph isomorphism|isomorphic]] to <math>H</math>.
Subgraph isomorphism is a generalization of both the [[clique problem|maximum clique problem]] and the problem of testing whether a graph contains a [[Hamiltonian cycle]], and is therefore [[NP-complete]].<ref>The original {{harvtxt|Cook|1971}} paper that proves the [[Cook–Levin theorem]] already showed subgraph isomorphism to be NP-complete, using a reduction from [[3-SAT]] involving cliques.</ref> However certain other cases of subgraph isomorphism may be solved in polynomial time.<ref name="e99"/>

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.