License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2020.9
URN: urn:nbn:de:0030-drops-121672
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12167/
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Arroyo, Alan ; Bensmail, Julien ; Richter, R. Bruce

Extending Drawings of Graphs to Arrangements of Pseudolines

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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 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.

BibTeX - Entry

@InProceedings{arroyo_et_al:LIPIcs:2020:12167,
  author =	{Alan Arroyo and Julien Bensmail and R. Bruce Richter},
  title =	{{Extending Drawings of Graphs to Arrangements of Pseudolines}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Sergio Cabello and Danny Z. Chen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12167},
  URN =		{urn:nbn:de:0030-drops-121672},
  doi =		{10.4230/LIPIcs.SoCG.2020.9},
  annote =	{Keywords: graphs, graph drawings, geometric graph drawings, arrangements of pseudolines, crossing numbers, stretchability}
}

Keywords: graphs, graph drawings, geometric graph drawings, arrangements of pseudolines, crossing numbers, stretchability
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020

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