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

Abstract : We prove that the dual graph of any arrangement of n lines in general position always contains a path of length at least n2/4. Further, 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 simple path through at least n cells where red and blue lines are crossed alternatingly.
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Submitted on : Monday, August 31, 2015 - 5:03:14 PM
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Oswin Aichholzer, Jean Cardinal, Thomas Hackl, Ferran Hurtado, Matias Korman, et al.. Cell-paths in mono- and bichromatic line arrangements in the plane. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 3 (in progress) (3), pp.317--322. ⟨hal-01188902⟩

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