Efficient Planarity Testing
Hopcroft, John E.; Tarjan, Robert Endre
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 uses 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 successfully tested graphs with as many as 900 vertices in less than 12 seconds.
computer science; technical report
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