Primitive Illumination Systems for Families of Convex Bodies in the Plane

Let F= {C1,C2,...,C} be a family of ndisjoint convex bodies in the plane. We say that a set Vof exterior light sources illuminates F, if for every boundary point ν of any member of Fthere is a point ν in Vsuch that υ is visible from ν,i.e. the open line segment joining ν and υ is disjoint from ∪ F. An illumination system Vis called primitive if no proper subset of Villuminates F. Let pmax(F) denote the maximum number of points forming a primitive illumination system for F, and letpmax(n) denote the minimum of F) taken over all families Fconsisting of ndisjoint convex bodies in the plane. The aim of this paper is to investigate the quantities pmax(F) and pmax(n).