An SPQR-Tree-Like Embedding Representation for Upward Planarity

  • Guido BrücknerEmail author
  • Markus Himmel
  • Ignaz Rutter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)


The SPQR-tree is a data structure that compactly represents all planar embeddings of a biconnected planar graph. It plays a key role in constrained planarity testing.

We develop a similar data structure, called the UP-tree, that compactly represents all upward planar embeddings of a biconnected single-source directed graph. We demonstrate the usefulness of the UP-tree by solving the upward planar embedding extension problem for biconnected single-source directed graphs.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Karlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.University of PassauPassauGermany

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