Extending Drawings of Graphs to Arrangements of Pseudolines

Alan Arroyo (1) , Julien Bensmail (2) , Bruce R. Richter (3)

1 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]
2 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
3 University of Waterloo [Waterloo]

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.

Mots clés: graphs; graph drawings; geometric graph drawings; arrangements of pseudolines; crossing numbers; stretchability

Domaines: Mathématique discrète [cs.DM]

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⟩