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

Schaefer, Marcus (2014) Picking Planar Edges; or, Drawing a Graph with a Planar Subgraph. In: Graph Drawing 22nd International Symposium, GD 2014, September 24-26, 2014, Würzburg, Germany , pp. 13-24 (Official URL: http://dx.doi.org/10.1007/978-3-662-45803-7_2).

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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.

Item Type:Conference Paper
Additional Information:10.1007/978-3-662-45803-7_2
Classifications:G Algorithms and Complexity > G.420 Crossings
G Algorithms and Complexity > G.770 Planarity Testing
P Styles > P.600 Poly-line
P Styles > P.720 Straight-line
Z Theory > Z.750 Topology
ID Code:1418

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