Long Alternating Paths in Bicolored Point Sets

Given n red and n blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length n + c n log n . We disprove a conjecture of Erd˝os by constructing an example without any such path of length greater than 4 3 n + c √ n.

• Type: Conference
• Year: 2004
• Where: GD
• Authors: Jan Kyncl, János Pach, Géza Tóth
• Keywords: Blue Points, Convex Position, GD 2004, Noncrossing Alternating Path