A Lower Bound for an Erdös-Szekeres-Type Problem with Interior Points
Banyat Sroysang · 2011
A point of a finite planar point set is called an interior point of the set if it is not on the boundary of the convex hull of the set. For any positive integer n, let g(n) be the smallest integer such that every planar point set P with no three collinear points and with at least g(n) interior points has a subset Q whose the interior of the convex hull of Q contains exactly n points of P. In this paper, we prove that g(n) 4n for all n 4.