Algorithms and Bounds for Drawing Non-planar Graphs with Crossing-free Subgraphs

Construction of 3-bend Compatible Drawings

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 and drawing area are given.

References:

• Patrizio Angelini, Carla Binucci, Giordano Da Lozzo, Walter Didimo, Luca Grilli, Fabrizio Montecchiani and Maurizio Patrignani, Ioannis Tollis. Algorithms and Bounds for Drawing Non-planar Graphs with Crossing-free Subgraphs. Technical Report arXiv:1308.6706, Cornell University, 2013.
• Patrizio Angelini, Carla Binucci, Giordano Da Lozzo, Walter Didimo, Luca Grilli, Fabrizio Montecchiani, Maurizio Patrignani, Ioannis Tollis. Drawing Non-planar Graphs with Crossing-free Subgraphs. In, Stephen Wismath, Alexander Wolff, editors, Proc. 21st International Symposium on Graph Drawing (GD ’13), Springer-Verlag, volume 8242 of Lecture Notes in Computer Science, pages 295-307, 2013.