Long monotone paths in line arrangements

We show how to construct an arrangement of n lines having a monotone path of length Ω(n2−(d/ √ log n)), where d > 0 is some constant, and thus nearly settle the long standing question on monotone path length in line arrangements.

• Type: Conference
• Year: 2003
• Where: COMPGEOM
• Authors: József Balogh, Oded Regev, Clifford D. Smyth, William L. Steiger, Mario Szegedy
• Keywords: COMPGEOM 2003, Long Standing Question, Monotone Path, Monotone Path Length