scholarly journals Searching for empty convex polygons

Algorithmica ◽  
1990 ◽  
Vol 5 (1-4) ◽  
pp. 561-571 ◽  
Author(s):  
David P. Dobkin ◽  
Herbert Edelsbrunner ◽  
Mark H. Overmars
Keyword(s):  
Convex Polygons ◽  
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 Empty convex polygons in almost convex sets

2007 ◽  
Vol 55 (2) ◽  
pp. 121-127 ◽  
Author(s):  
Pavel Valtr ◽  
Gábor Lippner ◽  
Gyula Károlyi
Keyword(s):  
Convex Sets ◽  
Convex Polygons ◽  
Empty Convex ◽  
Almost Convex

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

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.

Sign in / Sign up

Export Citation Format

Share Document