Primitive Illumination Systems for Families of Convex Bodies in the Plane

Let F = fC 1 ; C 2 ; : : : ; C n g be a family of n disjoint convex bodies in the plane. We say that a set V of exterior light sources illuminates F, if for every boundary point u of any member of F there is a point v in V such that u is visible from v, i.e. the open line segment joining u and v is disjoint from F. An illumination system V is called primitive if no 1 2 Valeriu Soltan, LL aszll o Szabb o, Eva VV ass arhelyi proper subset of V illuminates F. Let p max (F) denote the maximum number of points forming a primitive illumination system for F, and let p max (n) denote the minimum of p max (F) taken over all families F consisting of n disjoint convex bodies in the plane. The aim of this paper is to investigate the quantities p max (F) and p max (n).