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.2019.32
URN: urn:nbn:de:0030-drops-104363
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10436/
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Eppstein, David

Cubic Planar Graphs That Cannot Be Drawn On Few Lines

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LIPIcs-SoCG-2019-32.pdf (0.8 MB)


Abstract

For every integer l, we construct a cubic 3-vertex-connected planar bipartite graph G with O(l^3) vertices such that there is no planar straight-line drawing of G whose vertices all lie on l lines. This strengthens previous results on graphs that cannot be drawn on few lines, which constructed significantly larger maximal planar graphs. We also find apex-trees and cubic bipartite series-parallel graphs that cannot be drawn on a bounded number of lines.

BibTeX - Entry

@InProceedings{eppstein:LIPIcs:2019:10436,
  author =	{David Eppstein},
  title =	{{Cubic Planar Graphs That Cannot Be Drawn On Few Lines}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{32:1--32:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10436},
  URN =		{urn:nbn:de:0030-drops-104363},
  doi =		{10.4230/LIPIcs.SoCG.2019.32},
  annote =	{Keywords: graph drawing, universal point sets, collinearity}
}

Keywords: graph drawing, universal point sets, collinearity
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019


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