Discrete & Computational Geometry

, Volume 32, Issue 2, pp 167–176

Long Monotone Paths in Line Arrangements


DOI: 10.1007/s00454-004-1119-1

Cite this article as:
Balogh, J., Regev, O., Smyth, C. et al. Discrete Comput Geom (2004) 32: 167. doi:10.1007/s00454-004-1119-1


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.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Mathematics, The Ohio State University, Columbus, OH 43210USA
  2. 2.EECS Department, University of California at Berkeley, Berkeley, CA 94720USA
  3. 3.Department of Mathematical Sciences, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213USA
  4. 4.Department of Computer Science, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08854USA

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