Article Title：Art gallery theorems for guarded guards
Abstract：
We prove two art gallery theorems in which the guards must guard one another in addition to the gallery. A set g of points (the guards) in a simple closed polygon (the art gallery) is a guarded guard set provided (i) every point in the polygon is visible to some point in G; and (ii) every point in G is visible to some other point in G. We prove that a polygon with n sides always has a guarded guard set of cardinality [(3n - 1)/7] and that this bound is sharp (n greater than or equal to 5); our result corrects an erroneous formula in the literature. We also use a coloring argument to give an entirely new proof that the corresponding sharp function for orthogonal polygons is [n/3] for n greater than or equal to 6; this result was originally established by induction by Hernandez-Penalver. (C) 2003 Elsevier B.V. All rights reserved.
Keywords: art gallery theorems; visibility in polygons
DOI: 10.1016/S0925-7721(03)00039-7
Source：COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS
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