In this paper we consider a variation of the Art Gallery Problem. A set of points G in a polygon P_n is a connected guard set for P_n provided that is a guard set and the visibility graph of the set of guards G in P_n is connected. We use a coloring argument to prove that the minimum number of connected guards which are necessary to watch any polygon with n sides is [(n ― 2)/2]. This result was originally established by induction by Hernandez-Penalver. From this result it easily follows that if the art gallery is orthogonal (each interior angle is 90° or 270° ), then the minimum number of connected guards is n/2 ― 2.
展开▼
