On the Complexity of HV-rectilinear Planarity Testing

  • Walter Didimo
  • Giuseppe Liotta
  • Maurizio Patrignani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)


An HV-restricted planar graph G is a planar graph with vertex-degree at most four and such that each edge is labeled either H (horizontal) or V (vertical). The HV-rectilinear planarity testing problem asks whether G admits a planar drawing where every edge labeled V is drawn as a vertical segment and every edge labeled H is drawn as a horizontal segment. We prove that HV-rectilinear planarity testing is NP-complete even for graphs having vertex degree at most three, which solves an open problem posed by both Manuch et al. (GD 2010) and Durucher et al. (LATIN 2014). We also show that HV-rectilinear planarity can be tested in polynomial time for partial 2-trees of maximum degree four, which extends a previous result by Durucher et al. (LATIN 2014) about HV-restricted planarity testing of biconnected outerplanar graphs of maximum degree three. When the test is positive, our algorithm returns an orthogonal representation of G that satisfies the given H- and V-labels on the edges.


Planarity Testing External Face Planar Embedding Orthogonal Representation Biconnected Component 
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-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Walter Didimo
    • 1
  • Giuseppe Liotta
    • 1
  • Maurizio Patrignani
    • 2
  1. 1.Dept. of EngineeringUniversity of PerugiaItaly
  2. 2.Dept. of EngineeringRoma Tre UniversityItaly

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