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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
##### Keywords:
noncrossing alternating path; bicolored point set
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##### References:
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