K-Guarding Polygons on the Plane.
Patrice Belleville, Prosenjit K. Bose, Jurek Czyzowicz, Jorge Urrutia, Joseph Zaks · Canadian Conference on Computational Geometry · 1994
Let P be a simple polygon with n vertices. We say that P is k-guardable if it is possible to find a set of points Q consisting of interior points of edges of P such that every point of P is visible from at least k elements in Q and no edge of P has more than one element in Q. The following question was asked by A. Lubiw at the open problem session of the Fourth Canadian Conference in Computational Geometry: For what values of k, is every simple polygon k-guardable? It has been observed by T. Shermer that comb polygons [Chv75, O'R87] are not 3-guardable; such a polygon is shown in Figure 1.