Note on the paper "K-vertex guarding simple polygons" [Computational Geometry 42 (4) (May 2009) 352-361]

A polygon P is called k-vertex guardable if there is a subset G of the vertices of P such that each point in P is seen by at least k vertices in G . For the main results of this paper, it is shown that the following number of vertex guards is sufficient and sometimes necessary to k-vertex guard any simple n-gon P without holes: 2n/3 are needed for k = 2 if P is any n-gon and 3n/4 are needed for k = 3 if P is any convexly quadrilateralizable n-gon. The proofs for both of the results yield algorithms with O (n2) runtimes.