Blocking the k-Holes of Point Sets in the Plane

1 Let P be a set of n points in the plane in general position. A 2 subset H of P consisting of k elements that are the vertices of a convex 3 polygon is called a k-hole of P , if there is no element of P in the interior 4 of its convex hull. A set B of points in the plane blocks the k-holes of 5 P if any k-hole of P contains at least one element of B in the interior 6 of its convex hull. In this paper we establish upper and lower bounds 7 on the sizes of k-hole blocking sets, with emphasis in the case k = 5. 8