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Journal Articles Journal of Computational Geometry Year : 2021

Extending Drawings of Graphs to Arrangements of Pseudolines

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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Dates and versions

hal-03120899 , version 1 (25-01-2021)

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Alan Arroyo, Julien Bensmail, Bruce R. Richter. Extending Drawings of Graphs to Arrangements of Pseudolines. Journal of Computational Geometry, 2021, 12 (2), pp.3-24. ⟨10.20382/jocg.v12i2a2⟩. ⟨hal-03120899⟩
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