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Open AccessArticle

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

Faculty of Accounting, Shanxi University of Finance and Economics, Taiyuan 030006, China
College of Computer Science and Engineering, Dalian Minzu University, Dalian 116600, China
College of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, China
Author to whom correspondence should be addressed.
Symmetry 2018, 10(10), 447;
Received: 6 September 2018 / Revised: 23 September 2018 / Accepted: 26 September 2018 / Published: 29 September 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
PDF [1715 KB, uploaded 29 September 2018]


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. View Full-Text
Keywords: planar point set; convex polygon; disjoint holes planar point set; convex polygon; disjoint holes

Figure 1

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Yang, Q.; You, Z.; You, X. A Note on the Minimum Size of a Point Set Containing Three Nonintersecting Empty Convex Polygons. Symmetry 2018, 10, 447.

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