ABSTRACT
An extremal case of this problem was studied by Horton [4] who showed that it was not possible in general to specify both the number of hull vertices and the number of interior points: there exist arbitrarily large point sets P which do not contain at least 7 vertices of any convex polygon whose interior is disjoint from P, This result has very recently been extended by Nyklová [6], see also [2] for a survey of related problems.
