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A Note on the Minimum Size of a Point Set Containing Three Nonintersecting Empty Convex Polygons

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Let P be a planar point set with no three points collinear, k points of P be a k-hole of P if the k points are the vertices of a… Click to show full abstract

Let P be a planar point set with no three points collinear, k points of P be a k-hole of P if the k points are the vertices of a convex polygon without points of P. This article proves 13 is the smallest integer such that any planar points set containing at least 13 points with no three points collinear, contains a 3-hole, a 4-hole and a 5-hole which are pairwise disjoint.

Keywords: containing three; point set; set containing; minimum size; note minimum; size point

Journal Title: Symmetry
Year Published: 2018

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