Guarding the Convex Subsets of a Point-set
نویسندگان
چکیده
A point in the plane is called a guard for the convex set C if it lies in the interior of C. Let P be a planar point-set. A set S of points is a k-convex guard set for P if every convex k-gon formed from points of P contains a guard from S. We study, for any integer k 3, the minimum size of a k-convex guard set of a given planar point-set of size n. We give the tight bounds for the case k = 3, for any arrangement of n points, c of which form their convex hull. We prove that, in this case, 2n?c?2 guards are always necessary and suucient to cover all the triangles having vertices from P.
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