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.2018.68
URN: urn:nbn:de:0030-drops-87818
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8781/
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Pach, János ; Reed, Bruce ; Yuditsky, Yelena

Almost All String Graphs are Intersection Graphs of Plane Convex Sets

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LIPIcs-SoCG-2018-68.pdf (0.6 MB)

Abstract

A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n --> infty). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.

BibTeX - Entry

@InProceedings{pach_et_al:LIPIcs:2018:8781,
  author =	{J{\'a}nos Pach and Bruce Reed and Yelena Yuditsky},
  title =	{{Almost All String Graphs are Intersection Graphs of Plane Convex Sets}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{68:1--68:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8781},
  URN =		{urn:nbn:de:0030-drops-87818},
  doi =		{10.4230/LIPIcs.SoCG.2018.68},
  annote =	{Keywords: String graph, intersection graph, plane convex set}
}

Keywords: String graph, intersection graph, plane convex set
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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