scholarly journals Disjoint empty convex polygons in planar point sets

2001 ◽  
Vol 56 (2) ◽  
pp. 62-70
Author(s):  
Attila Guly�s ◽  
L�zl� Szab�
Keyword(s):  
Point Sets ◽  
Convex Polygons ◽  
Planar Point ◽  
Empty Convex

Planar point sets with a small number of empty convex polygons

2004 ◽  
Vol 41 (2) ◽  
pp. 243-269 ◽  
Author(s):  
Imre Bárány ◽  
Pável Valtr
Keyword(s):  
Convex Hull ◽  
General Position ◽  
Point Sets ◽  
Convex Polygons ◽  
Planar Point ◽  
Empty Convex ◽  
Finite Set ◽  
Empty Triangles

A subset A of a finite set P of points in the plane is called an empty polygon, if each point of A is a vertex of the convex hull of A and the convex hull of A contains no other points of P. We construct a set of n points in general position in the plane with only ˜1.62n2 empty triangles, ˜1.94n2 empty quadrilaterals, ˜1.02n2 empty pentagons, and ˜0.2n2 empty hexagons.

scholarly journals Disjoint empty convex pentagons in planar point sets

2012 ◽  
Vol 66 (1) ◽  
pp. 73-86 ◽  
Author(s):  
Bhaswar B. Bhattacharya ◽  
Sandip Das
Keyword(s):  
Point Sets ◽  
Planar Point ◽  
Empty Convex

scholarly journals EMPTY CONVEX 5-GONS IN PLANAR POINT SETS

2009 ◽  
Vol 31 (3) ◽  
pp. 315-321
Author(s):  
Seong-Yoon Ann ◽  
En-Sil Kang
Keyword(s):  
Point Sets ◽  
Planar Point ◽  
Empty Convex

Counting convex polygons in planar point sets

1995 ◽  
Vol 56 (1) ◽  
pp. 45-49 ◽  
Author(s):  
Joseph S.B. Mitchell ◽  
Günter Rote ◽  
Gopalakrishnan Sundaram ◽  
Gerhard Woeginger
Keyword(s):  
Point Sets ◽  
Convex Polygons ◽  
Planar Point

scholarly journals On empty convex polygons in a planar point set

2006 ◽  
Vol 113 (3) ◽  
pp. 385-419 ◽  
Author(s):  
Rom Pinchasi ◽  
Radoš Radoičić ◽  
Micha Sharir
Keyword(s):  
Convex Polygons ◽  
Planar Point ◽  
Empty Convex ◽  
Point Set

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

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 447
Author(s):  
Qing Yang ◽  
Zengtai You ◽  
Xinshang You
Keyword(s):  
Pairwise Disjoint ◽  
Convex Polygon ◽  
Minimum Size ◽  
Convex Polygons ◽  
Planar Point ◽  
Empty Convex ◽  
Point Set

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.

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