Bitonic st-orderings for Upward Planar Graphs

  • Martin GronemannEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)


Canonical orderings serve as the basis for many incremental planar drawing algorithms. All these techniques, however, have in common that they are limited to undirected graphs. While st-orderings do extend to directed graphs, especially planar st-graphs, they do not offer the same properties as canonical orderings. In this work we extend the so called bitonic st-orderings to directed graphs. We fully characterize planar st-graphs that admit such an ordering and provide a linear-time algorithm for recognition and ordering. If for a graph no bitonic st-ordering exists, we show how to find in linear time a minimum set of edges to split such that the resulting graph admits one. With this new technique we are able to draw every upward planar graph on n vertices by using at most one bend per edge, at most \(n - 3\) bends in total and within quadratic area.


Directed Graph Planar Graph Span Subgraph Canonical Ordering Quadratic Area 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.University of CologneCologneGermany

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