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Subgraph isomorphism in planar graphs and related problems. (English) Zbl 0949.05055
Summary: 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.

MSC:
05C60Isomorphism problems (graph theory)
06C10Semimodular lattices, geometric lattices
90C39Dynamic programming