Almost all string graphs are intersection graphs of plane convex sets

János Pach, Bruce Reed, Yelena Yuditsky

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 α→ ∞). 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.

Original languageEnglish
Title of host publication34th International Symposium on Computational Geometry, SoCG 2018
EditorsCsaba D. Toth, Bettina Speckmann
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages681-6814
Number of pages6134
ISBN (Electronic)9783959770668
DOIs
StatePublished - 1 Jun 2018
Externally publishedYes
Event34th International Symposium on Computational Geometry, SoCG 2018 - Budapest, Hungary
Duration: 11 Jun 201814 Jun 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume99
ISSN (Print)1868-8969

Conference

Conference34th International Symposium on Computational Geometry, SoCG 2018
Country/TerritoryHungary
CityBudapest
Period11/06/1814/06/18

Keywords

  • Intersection graph
  • Plane convex set
  • String graph

ASJC Scopus subject areas

  • Software

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