In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs and are given as input, and one must determine whether contains a subgraph that is isomorphic to . 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. However certain other cases of subgraph isomorphism may be solved in polynomial time.