Before revision: A k-hole in a point set S \subseteq R^2 is a subset X \subseteq S, |X|=k, such that all points of X lie on the boundary of the convex hull conv (X) and no point of S \setminus X lies in conv (X).
After revision: Given a set of points S \subseteq R^2 is a subset X \subseteq S, |X|=k, such that all points of X lie on the boundary of the convex hull conv (X) and no point of S \setminus X lies in conv (X).