Cell-paths in mono- and bichromatic line arrangements in the plane

Oswin Aichholzer, Jean Cardinal, Thomas Hackl, Ferran Hurtado, Matias Korman, Alexander Pilz, Rodrigo I. Silveira, Ryuhei Uehara, Birgit Vogtenhuber, Emo Welzl

Research output: Contribution to conferencePaper

Abstract

We show that in every arrangement of n red and blue lines-in general position and not all of the same color-there is a path through a linear number of cells where red and blue lines are crossed alternatingly (and no cell is revisited). When all lines have the same color, and hence the preceding alternating constraint is dropped, we prove that the dual graph of the arrangement always contains a path of length θ(n2).

Original languageEnglish
Pages169-174
Number of pages6
Publication statusPublished - 2013 Jan 1
Externally publishedYes
Event25th Canadian Conference on Computational Geometry, CCCG 2013 - Waterloo, Canada
Duration: 2013 Aug 82013 Aug 10

Other

Other25th Canadian Conference on Computational Geometry, CCCG 2013
CountryCanada
CityWaterloo
Period13/8/813/8/10

ASJC Scopus subject areas

  • Geometry and Topology
  • Computational Mathematics

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    Aichholzer, O., Cardinal, J., Hackl, T., Hurtado, F., Korman, M., Pilz, A., Silveira, R. I., Uehara, R., Vogtenhuber, B., & Welzl, E. (2013). Cell-paths in mono- and bichromatic line arrangements in the plane. 169-174. Paper presented at 25th Canadian Conference on Computational Geometry, CCCG 2013, Waterloo, Canada.