Cell-Paths in Mono- and Bichromatic Line Arrangements in the Plane

@article{Aichholzer2013CellPathsIM,
  title={Cell-Paths in Mono- and Bichromatic Line Arrangements in the Plane},
  author={Oswin Aichholzer and Jean Cardinal and Thomas Hackl and Ferran Hurtado and Matias Korman and Alexander Pilz and Rodrigo I. Silveira and Ryuhei Uehara and Birgit Vogtenhuber and Emo Welzl},
  journal={Discrete Mathematics & Theoretical Computer Science},
  year={2013},
  volume={16},
  pages={317-332}
}
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(n). 

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