Abstract

An efficient algorithm is presented for determining whether or not a given graph is planar. If V is the number of vertices in the graph, the algorithm requires time proportional to V log V and space proportional to V when run on a random-access computer. The algorithm constructs the facial boundaries of a planar representation without backup, using extensive list-processing features to speed computation. The theoretical time bound improves on that of previously published algorithms. Experimental evidence indicates that graphs with a few thousand edges can be tested within seconds.