Outerstring graphs are Χ-bounded

Alexandre Rok, Bartosz Walczak

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

16 Scopus citations


An outerstring graph is an intersection graph of curves lying in a halfplane with one endpoint on the boundary of the halfplane. It is proved that the outerstring graphs are Χ-bounded, that is, their chromatic number is bounded by a function of their clique number. This generalizes a series of previous results on Χ-boundedness of outerstring graphs with various restrictions of the shape of the curves or the number of times the pairs of curves can intersect. This also implies that the intersection graphs of x-monotone curves with bounded clique number have chromatic number O(log n), improving the previous polylogarithmic upper bound. The assumption that each curve has an endpoint on the boundary of the halfplane is justified by the known fact that triangle-free intersection graphs of straight-line segments can have arbitrarily large chromatic number. Copyright is held by the owner/author(s).

Original languageEnglish
Title of host publicationProceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014
PublisherAssociation for Computing Machinery
Number of pages8
ISBN (Print)9781450325943
StatePublished - 1 Jan 2014
Externally publishedYes
Event30th Annual Symposium on Computational Geometry, SoCG 2014 - Kyoto, Japan
Duration: 8 Jun 201411 Jun 2014

Publication series

NameProceedings of the Annual Symposium on Computational Geometry


Conference30th Annual Symposium on Computational Geometry, SoCG 2014


  • Chromatic number
  • Geometric intersection graphs
  • Outerstring graphs
  • Χ-boundedness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics


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