In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a subgraph that is isomorphic to H.
Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete.[1] However certain other cases of subgraph isomorphism may be solved in polynomial time.[2]
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.
^The original 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.
^Cite error: The named reference e99 was invoked but never defined (see the help page).
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