2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33325We 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.27 pages, 6 figures. A preliminary version of this paper appeared at the 6th ACM-SIAM Symp. Discrete Algorithms, 1995Data Structures and AlgorithmsF.2.2text