More on planar point subsets with a specified number of interior points
Xianglin Wei, Рен Динг · Mathematical Notes · 2008
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 g ( k ) be the smallest integer such that every set P of points in the plane with no three collinear points and with at least g ( k ) interior points has a subset containing precisely k interior point of P . We prove that g ( k ) ≥ 3 k for k ≥ 3, which improves the known result that g ( k ) ≥ 3 k − 1 for k ≥ 3.