On the existence of a point subset with three or five interior points
Xianglin Wei, Wenhua Lan, Рен Динг · Mathematical Notes · 2010
An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let h ( k ) be the smallest integer such that every point set in the plane, no three collinear, with at least h ( k ) interior points, has a subset with k or k + 2 interior points of P . We prove that h (3) = 8.