On the Minimum Size of a Point Set Containing Two Non-intersecting Empty Convex Polygons

摘要

Let n(k, l) be the smallest integer such that any set of n(k, l) points in the plane, no three collinear, contains both an empty convex k-gon and an empty convex l-gon, which do not intersect. We show that n(3,5) = 10, 12 ≤ n(4,5) ≤ 14, 16 ≤ n(5,5) ≤ 20.