Bitonic st-orderings of Biconnected Planar Graphs

Vertex orderings play an important role in the design of graph drawing algorithms. Compared to canonical orderings, st-orderings lack a certain property that is required by many drawing methods. In this paper, we propose a new type of st-ordering for biconnected planar graphs that relates the ordering to the embedding. We describe a linear-time algorithm to obtain such an ordering and demonstrate its capabilities with two applications.