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Long alternating paths in bicolored point sets. (English) Zbl 1168.05320
Summary: Given \(n\) red and \(n\) blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length \(n+c\sqrt{n/\log n}\). We disprove a conjecture of Erdős by constructing an example without any such path of length greater than \(4/3 n + c'\sqrt n\).

MSC:
05C38 Paths and cycles
05C15 Coloring of graphs and hypergraphs
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