Recognizing small subgraphs

Although the general problem of subgraph isomorphismis NP-complete, polynomial-time algorithms exist for recognizing any xed subgraph. However, certain subgraphs appear easier to recognize than others. In this paper, we present general algorithms for xed-subgraph isomorphism which improve or unify previous results. In particular, we present an O(n f m) algorithm for recognizing a xed subgraph H with ower number f within a graph G with n vertices and m edges. Special cases of this algorithm match the best algorithms known for recognizing small paths, cycles, and cliques. Further, we improve previous results for recognizing C 5 and small even cycles C 2k , k 3.