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Subgraph Isomorphism in Planar Graphs and Related Problems

David Eppstein
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Abstract

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.

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David Eppstein. 1999-11-09. Subgraph Isomorphism in Planar Graphs and Related Problems. https://arxiv.org/abs/cs/9911003

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