Note on noncrossing path in colored convex sets ∗
نویسندگان
چکیده
Consider a 2n element colored point set, n points red and n points blue, in convex position in the plane. Erdős asked to estimate the number of points in the longest noncrossing path such that edges join points of different color and are straight line segments. Kynčl, Pach and Tóth in 2008 gave a construction proving the upper bound 43n+ O( √ n). This bound is conjectured to be tight. For an arbitrary coloring they gave a lower bound n+Ω( √
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Separated matchings on colored convex sets
Erdős posed the following problem. Consider an equicolored point set of 2n points, n points red and n points blue, in the plane in convex position. We estimate the minimal number of points on the longest noncrossing path such that edges join points of different color and are straight line segments. The upper bound 4 3 n + O( √ n) is proved [7], [5] and is conjectured to be tight. The best known...
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