Algorithms
Ullmann (1976) describes a recursive backtracking procedure for solving the subgraph isomorphism problem. Although its running time is, in general, exponential, it takes polynomial time for any fixed choice of H (with a polynomial that depends on the choice of H). When G is a planar graph and H is fixed, the running time of subgraph isomorphism can be reduced to linear time.
Read more about this topic: Subgraph Isomorphism Problem