Next Article in Journal
Eventually DSDD Matrices and Eigenvalue Localization
Next Article in Special Issue
The Structure Theorems of Pseudo-BCI Algebras in Which Every Element is Quasi-Maximal
Previous Article in Journal
Statistical Inference for the Information Entropy of the Log-Logistic Distribution under Progressive Type-I Interval Censoring Schemes
Previous Article in Special Issue
Multi-Granulation Graded Rough Intuitionistic Fuzzy Sets Models Based on Dominance Relation
Open AccessArticle

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

1
Faculty of Accounting, Shanxi University of Finance and Economics, Taiyuan 030006, China
2
College of Computer Science and Engineering, Dalian Minzu University, Dalian 116600, China
3
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; https://doi.org/10.3390/sym10100447
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]
  |  

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

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

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.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top