Embedding planar graphs using PQ-tree algorithms

The problems of testing the planarity of a graph and of embedding a planar graph in a plane arise in many applications. This paper presents a simple linear algorithm for the latter problem. the algorithm is based on the “vertex‐addition algorithm” of Lempel, Even and Cederbaum for planarity testing and is a slight modification of Booth and Lueker's implementation of the testing algorithm using a PQ‐tree. Compared with the embedding algorithm known as the “path‐addition” algorithm of Hopcroft and Tarjan, our algorithm is conceptually simple and easy to understand or implement.