# Parallel algorithms for the subgraph homeomorphism problem

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## Abstract

The subgraph homeomorphism problem for a fixed graph *H* is stated as follows: given a graph *G*, determine whether *G* has a subgraph homeomorphic to *H*, and obtain it. We study the parallel complexity of this problem for various pattern graphs *H*, and present fast *NC* algorithms for various versions of this problem. We also present an efficient *NC* algorithm to check if a given graph is outer-planar and to obtain its forbidden homeomorphs *K*_{4} or *K*_{2,3}, if it is not.

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© Springer-Verlag Berlin Heidelberg 1989