An Improved Algorithm for Testing the Planarity of a Graph

Hopcroft and Tarjan [2] have recently proposed an algorithm that runs in linear time for testing the planarity of a graph. The technique finds a representation of the graph as a sequence of paths and then iteratively imbeds these paths to find a mesh structure, rearranging the meshes as needed to accommodate each new path. Demoucron et al. [1] have shown that this rearrangement process is unnecessary if the paths are considered in the proper order. The present implementation is found to run in linear time for most ordinary cases, about twice as fast as Tarjan's Algol implementation. A graph of 3000 vertices and 8994 edges required about 18 s.