On the Existence of a Point Subset with 3 or 7 Interior Points
Banyat Sroysang · 2012
An interior point of a planar point set P is a point of P such that it is not on the boundary of the convex hull of P. For each integer k ≥ 3, let h(k) be the smallest integer such that every finite planar point set P with no three collinear points and with at least h(k) interior points has a subset Q whose the interior of the convex hull of Q contains exactly k or k + 4 interior points of P. In this paper, we show that h(3) = 7.