Coloring curves that cross a fixed curve

Alexandre Rok, Bartosz Walczak

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

2 Scopus citations

Abstract

We prove that for every integer t ≧ 1, the class of intersection graphs of curves in the plane each of which crosses a fixed curve in at least one and at most t points is χ-bounded. This is essentially the strongest χ-boundedness result one can get for this kind of graph classes. As a corollary, we prove that for any fixed integers k ≧ 2 and t ≧ 1, every k-quasi-planar topological graph on n vertices with any two edges crossing at most t times has O(n log n) edges.

Original languageEnglish
Title of host publication33rd International Symposium on Computational Geometry, SoCG 2017
EditorsMatthew J. Katz, Boris Aronov
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages561-5615
Number of pages5055
ISBN (Electronic)9783959770385
DOIs
StatePublished - 1 Jun 2017
Event33rd International Symposium on Computational Geometry, SoCG 2017 - Brisbane, Australia
Duration: 4 Jul 20177 Jul 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume77
ISSN (Print)1868-8969

Conference

Conference33rd International Symposium on Computational Geometry, SoCG 2017
Country/TerritoryAustralia
CityBrisbane
Period4/07/177/07/17

Keywords

  • K-quasi-planar graphs
  • String graphs
  • χ-boundedness

ASJC Scopus subject areas

  • Software

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