Abstract
Given a graph G and a subset FâââE(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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Schaefer, M. (2014). Picking Planar Edges; or, Drawing a Graph with a Planar Subgraph. In: Duncan, C., Symvonis, A. (eds) Graph Drawing. GD 2014. Lecture Notes in Computer Science, vol 8871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45803-7_2
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DOI: https://doi.org/10.1007/978-3-662-45803-7_2
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