Efficient Planarity Testing
John E. Hopcroft, Robert Endre Tarjan · Journal of the ACM · 1974
This paper describes an efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane. The algorithm may be viewed as an iterative version of a method originally proposed by Auslander and Parter and correctly formulated by Goldstein. The algorithm used depth-first search and has O ( V ) time and space bounds, where V is the number of vertices in G . An ALGOL implementation of the algorithm succesfully tested graphs with as many as 900 vertices in less than 12 seconds.