Drawings of Non-planar Graphs with Crossing-free Subgraphs

@article{Angelini2013DrawingsON,
  title={Drawings of Non-planar Graphs with Crossing-free Subgraphs},
  author={Patrizio Angelini and Carla Binucci and Giordano Da Lozzo and Walter Didimo and Luca Grilli and Fabrizio Montecchiani and Maurizio Patrignani and Ioannis G. Tollis},
  journal={CoRR},
  year={2013},
  volume={abs/1308.6706}
}
We initiate the study of the following problem: Given a non-planar graph G and a planar subgraph S of G, does there exist a straight-line drawing Γ of G in the plane such that the edges of S are not crossed in Γ? We give positive and negative results for different kinds of spanning subgraphs S of G. Moreover, in order to enlarge the subset of instances that admit a solution, we consider the possibility of bending the edges of G \ S; in this setting different trade-offs between number of bends… CONTINUE READING
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