English

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

Computational Geometry 2014-08-11 v2

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 {\Gamma} of G in the plane such that the edges of S are not crossed in {\Gamma} 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.

Keywords

Cite

@article{arxiv.1308.6706,
  title  = {Algorithms and Bounds for Drawing 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= {arXiv preprint arXiv:1308.6706},
  year   = {2014}
}

Comments

21 pages, 9 figures, extended version of 'Drawing Non-planar Graphs with Crossing-free Subgraphs' (21st International Symposium on Graph Drawing, 2013)

R2 v1 2026-06-22T01:17:52.550Z