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, Pavel Valtr, Birgit Vogtenhuber, Emo Welzl

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We prove that the dual graph of any arrangement of η lines in general position always contains a path of length at least n2/4. Further, we show that in every arrangement of η red and blue lines-in general position and not all of the same color-there is a simple path through at least η cells where red and blue lines are crossed alternatingly.

Original languageEnglish
Pages (from-to)317-332
Number of pages16
JournalDiscrete Mathematics and Theoretical Computer Science
Volume16
Issue number3
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Discrete geometry
  • Hamiltonicity
  • Line arrangement
  • Planar graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics

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