Extending Drawings of Graphs to Arrangements of Pseudolines

Alan Arroyo 1 Julien Bensmail 2 R. Bruce Richter 3
2 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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 Kn 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.
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Alan Arroyo, Julien Bensmail, R. Bruce Richter. Extending Drawings of Graphs to Arrangements of Pseudolines. SoCG 2020 - 36th International Symposium on Computational Geometry, Jun 2020, Zürich, Switzerland. ⟨hal-02471760⟩

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