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

  title={Picking Planar Edges; or, Drawing a Graph with a Planar Subgraph},
  author={Marcus Schaefer},
  booktitle={Graph Drawing},
Given a graph G and a subset F ⊆ E(G) of its edges, is there a drawing ofG 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, and allow at most 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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Toward a theory of crossing numbers

  • William T. Tutte
  • J. Combinatorial Theory,
  • 1970
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Über wesentlich unplättbare Kurven im drei-dimensionalen Raume

  • Chaim Chojnacki Haim Hanani
  • Fundamenta Mathematicae,
  • 1934
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