Coloring Curves that Cross a Fixed Curve

Alexandre Rok, Bartosz Walczak

Research output: Contribution to journalArticlepeer-review

6 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 those 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(nlog n) edges.

Original languageEnglish
Pages (from-to)830-851
Number of pages22
JournalDiscrete and Computational Geometry
Volume61
Issue number4
DOIs
StatePublished - 15 Jun 2019

Keywords

  • String graphs
  • k-Quasi-planar graphs
  • χ-Boundedness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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