Abstract

A graph is planar if it can be drawn on the plane with no crossing edges. There are several linear time planar embedding algorithms but all are considered by many to be quite complicated. This paper presents a new method for performing linear time planar graph embedding which avoids some of the complexities of previous approaches (including the need to first st-number the vertices). Our new algorithm easily permits the extraction of a planar obstruction (a subgraph homeomorphic to K3;3 or K5) in O(n) time if the graph is not planar. Our algorithm is similar to the algorithm of Booth and Lueker which uses a data structure called a PQ-tree. The Pnodes in a PQ-tree represent parts of the partially embedded graph that can be permuted, and the Q-nodes represent parts that can be flipped. We avoid the use of P-nodes by not connecting pieces together until they become biconnected. We avoid Q nodes by using a data structure which allows biconnected components to be flipped in O(1) time. 1 In...

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