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

Patrizio Angelini; Carla Binucci; Giordano Da Lozzo; Walter Didimo; Luca Grilli; Fabrizio Montecchiani; Maurizio Patrignani; Ioannis G. Tollis

arXiv · 1308.6706

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

Patrizio Angelini·Carla Binucci·Giordano Da Lozzo·Walter Didimo·Luca Grilli·Fabrizio Montecchiani·Maurizio Patrignani·Ioannis G. Tollis

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Abstract

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 by any edge of G? We give positive and negative results for different kinds of connected 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 not in S; in this setting we discuss different trade-offs between the number of bends and the required drawing area.

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Patrizio Angelini, Carla Binucci, Giordano Da Lozzo, Walter Didimo, Luca Grilli, Fabrizio Montecchiani, Maurizio Patrignani, Ioannis G. Tollis. 2014-08-07. Algorithms and Bounds for Drawing Non-planar Graphs with Crossing-free Subgraphs. https://arxiv.org/abs/1308.6706

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