Lecture Notes in Computer Science Volume 3383, 2005, pp 340-348

Long Alternating Paths in Bicolored Point Sets

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Given n red and n blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length $n+c\sqrt{n\over \log n}$ . We disprove a conjecture of Erdős by constructing an example without any such path of length greater than ${4\over 3}n+c'\sqrt{n}$ .