A note on coloring line arrangements

Eyal Ackerman, János Pach, Rom Pinchasi, Radoš Radoičić, Géza Tóth

Research output: Contribution to journalArticlepeer-review


We show that the lines of every arrangement of n lines in the plane can be colored with O colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a Θ(logn√) factor. Any further improvement on this bound would also improve the best known lower bound on the following problem of Erdo{double acute}s: estimate the maximum number of points in general position within a set of n points containing no four collinear points.

Original languageEnglish
JournalElectronic Journal of Combinatorics
Issue number2
StatePublished - 9 May 2014


  • Arrangements of lines
  • Chromatic number
  • Sparse hypergraphs

ASJC Scopus subject areas

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


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