Extending Drawings of Graphs to Arrangements of Pseudolines

Authors Alan Arroyo , Julien Bensmail, R. Bruce Richter

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Author Details

Alan Arroyo
  • IST Austria, Klosterneuburg, Austria
Julien Bensmail
  • Université Côte d'Azur, CNRS, Inria, I3S, Sophia-Antipolis, France
R. Bruce Richter
  • Department of Combinatorics and Optimization, University of Waterloo, Canada

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Alan Arroyo, Julien Bensmail, and R. Bruce Richter. Extending Drawings of Graphs to Arrangements of Pseudolines. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


In the recent study of crossing numbers, drawings of graphs that can be extended to an arrangement of pseudolines (pseudolinear drawings) have played an important role as they are a natural combinatorial extension of rectilinear (or straight-line) drawings. A characterization of the pseudolinear drawings of K_n was found recently. We extend this characterization to all graphs, by describing the set of minimal forbidden subdrawings for pseudolinear drawings. Our characterization also leads to a polynomial-time algorithm to recognize pseudolinear drawings and construct the pseudolines when it is possible.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Graphs and surfaces
  • graphs
  • graph drawings
  • geometric graph drawings
  • arrangements of pseudolines
  • crossing numbers
  • stretchability


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