Abstract
We show how to construct an arrangement of n lines having a monotone path of length Ω(n2 – (d/\sqrt{log n})), where d > 0 is some constant, and thus nearly settle the long standing question on monotone path length in line arrangements.
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Balogh, J., Regev, O., Smyth, C. et al. Long Monotone Paths in Line Arrangements. Discrete Comput Geom 32, 167–176 (2004). https://doi.org/10.1007/s00454-004-1119-1
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DOI: https://doi.org/10.1007/s00454-004-1119-1