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.MFCS.2017.47
URN: urn:nbn:de:0030-drops-80811
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8081/
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Hoffmann, Michael ; Tóth, Csaba D.

Two-Planar Graphs Are Quasiplanar

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LIPIcs-MFCS-2017-47.pdf (0.8 MB)

Abstract

It is shown that every 2-planar graph is quasiplanar, that is, if a simple graph admits a drawing in the plane such that every edge is crossed at most twice, then it also admits a drawing in which no three edges pairwise cross. We further show that quasiplanarity is witnessed by a simple topological drawing, that is, any two edges cross at most once and adjacent edges do not cross.

BibTeX - Entry

@InProceedings{hoffmann_et_al:LIPIcs:2017:8081,
  author =	{Michael Hoffmann and Csaba D. T{\'o}th},
  title =	{{Two-Planar Graphs Are Quasiplanar}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{47:1--47:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8081},
  URN =		{urn:nbn:de:0030-drops-80811},
  doi =		{10.4230/LIPIcs.MFCS.2017.47},
  annote =	{Keywords: graph drawing, near-planar graph, simple topological plane graph}
}

Keywords: graph drawing, near-planar graph, simple topological plane graph
Collection: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)
Issue Date: 2017
Date of publication: 01.12.2017

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