Abstract
We show that the maximal number of turns of anx-monotone path in an arrangement ofn lines is Ω(n 5/3) and the maximal number of turns of anx-monotone path in arrangement ofn pseudolines is Ω(n 2/logn).
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Matoušek, J. Lower bounds on the length of monotone paths in arrangements. Discrete Comput Geom 6, 129–134 (1991). https://doi.org/10.1007/BF02574679
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DOI: https://doi.org/10.1007/BF02574679