Extending Drawings of Graphs to Arrangements of Pseudolines

Alan Arroyo; Julien Bensmail; R. Bruce Richter

Conference papers

Extending Drawings of Graphs to Arrangements of Pseudolines

Alan Arroyo ¹ Julien Bensmail ² R. Bruce Richter ³

1 IST Austria - Institute of Science and Technology [Austria]

2 COATI - Combinatorics, Optimization and Algorithms for Telecommunications

CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués

3 University of Waterloo [Waterloo]

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.

Keywords : graph drawings geometric graph drawings arrangements of pseudolines crossing numbers stretchability graphs

Document type :

Conference papers

Domain :

Computer Science [cs] / Discrete Mathematics [cs.DM]

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https://hal.archives-ouvertes.fr/hal-02471760
Contributor : Julien Bensmail <>
Submitted on : Wednesday, February 19, 2020 - 2:28:02 PM
Last modification on : Tuesday, January 19, 2021 - 8:18:32 PM
Long-term archiving on: : Wednesday, May 20, 2020 - 3:56:15 PM

Extending Drawings of Graphs to Arrangements of Pseudolines

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Extending Drawings of Graphs to Arrangements of Pseudolines

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