, Volume 32, Issue 2, pp 167-176
Date: 07 Jun 2004

Long Monotone Paths in Line Arrangements

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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.