We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small tree-width, and applying dynamic programming within each piece. The same methods can be used to solve other planar graph problems including connectivity, diameter, girth, induced subgraph isomorphism, and shortest paths. Communicated by Roberto Tamassia: submitted December 1995, revised November 1999. Work supported in part by NSF grant CCR-9258355 and by matching funds from Xerox Corp. D. Eppstein, Planar Subgraph Isomorphism, JGAA, 3(3) 1-27 (1999) 2 1 Introduction Subgraph isomorphism is an important and very general form of exact pattern matching. Subgraph isomorphism is a common generalization of many important graph problems including nding Hamiltonian paths, cliques, matchings, girth, and shortest paths. Variations of subgraph isomorphism have also been used to model such...
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