Before revision: Given a set of points S \subseteq R^2, a subset X \subseteq S , |X|=k , is called k-gon if all points of X lie on the boundary of the convex hull \mathrm{conv , and k-hole if, in addition, no point of S \setminus X lies in \mathrm{conv .
After revision: Given a set of points S \subseteq R^2, a subset X \subseteq S , |X|=k , is called k-gon if all points of X lie on the boundary of the convex hull \mathrm{conv , and k-hole if, in addition, no point of S \setminus X lies in the convex hull of X .