Picking Planar Edges; or, Drawing a Graph with a Planar Subgraph

  • Marcus Schaefer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)


Given a graph G and a subset F ⊆ E(G) of its edges, is there a drawing of G in which all edges of F are free of crossings? We show that this question can be solved in polynomial time using a Hanani-Tutte style approach. If we require the drawing of G to be straight-line, but allow up to one crossing along each edge in F, the problem turns out to be as hard as the existential theory of the real numbers.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Marcus Schaefer
    • 1
  1. 1.School of ComputingDePaul UniversityChicagoUSA

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