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We prove a new theorem for orthogonal art galleries in which the guards must guard one another in addition to guarding the polygonal gallery. A set of points G in a polygon Pn is a k-guarded guard set for Pn provided that (i) for every point x in Pn there exists a point w in G such that x is visible from w ; and (ii) every point in G is visible from at least k other points in G: The polygon Pn is orthogonal provided each interior angle is 90掳 or 270掳. We prove that for k 驴 1 and n 驴 6 every orthogonal polygon with n sides has a k-guarded guard set of cardinality k驴n/6驴 + 驴(n+2)/6驴; this bound is best possible. This result extends our recent theorem that treats the case k = 1.

Multiply Guarded Guards in Orthogonal Art Galleries