A Note on the Minimum Size of a Point Set Containing Three Nonintersecting Empty Convex Polygons
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 colli...
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MDPI AG
2018-09-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/10/447 |
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doaj-c357b0e6518a4c82a55a658c83251bad2020-11-25T00:46:48ZengMDPI AGSymmetry2073-89942018-09-01101044710.3390/sym10100447sym10100447A Note on the Minimum Size of a Point Set Containing Three Nonintersecting Empty Convex PolygonsQing Yang0Zengtai You1Xinshang You2Faculty of Accounting, Shanxi University of Finance and Economics, Taiyuan 030006, ChinaCollege of Computer Science and Engineering, Dalian Minzu University, Dalian 116600, ChinaCollege of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, ChinaLet 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.http://www.mdpi.com/2073-8994/10/10/447planar point setconvex polygondisjoint holes |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Qing Yang Zengtai You Xinshang You |
| spellingShingle |
Qing Yang Zengtai You Xinshang You A Note on the Minimum Size of a Point Set Containing Three Nonintersecting Empty Convex Polygons Symmetry planar point set convex polygon disjoint holes |
| author_facet |
Qing Yang Zengtai You Xinshang You |
| author_sort |
Qing Yang |
| title |
A Note on the Minimum Size of a Point Set Containing Three Nonintersecting Empty Convex Polygons |
| title_short |
A Note on the Minimum Size of a Point Set Containing Three Nonintersecting Empty Convex Polygons |
| title_full |
A Note on the Minimum Size of a Point Set Containing Three Nonintersecting Empty Convex Polygons |
| title_fullStr |
A Note on the Minimum Size of a Point Set Containing Three Nonintersecting Empty Convex Polygons |
| title_full_unstemmed |
A Note on the Minimum Size of a Point Set Containing Three Nonintersecting Empty Convex Polygons |
| title_sort |
note on the minimum size of a point set containing three nonintersecting empty convex polygons |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2018-09-01 |
| description |
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. |
| topic |
planar point set convex polygon disjoint holes |
| url |
http://www.mdpi.com/2073-8994/10/10/447 |
| work_keys_str_mv |
AT qingyang anoteontheminimumsizeofapointsetcontainingthreenonintersectingemptyconvexpolygons AT zengtaiyou anoteontheminimumsizeofapointsetcontainingthreenonintersectingemptyconvexpolygons AT xinshangyou anoteontheminimumsizeofapointsetcontainingthreenonintersectingemptyconvexpolygons AT qingyang noteontheminimumsizeofapointsetcontainingthreenonintersectingemptyconvexpolygons AT zengtaiyou noteontheminimumsizeofapointsetcontainingthreenonintersectingemptyconvexpolygons AT xinshangyou noteontheminimumsizeofapointsetcontainingthreenonintersectingemptyconvexpolygons |
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