scholarly journals Levi's Lemma, pseudolinear drawings of Kn, and empty triangles

2017 ◽  
Vol 87 (4) ◽  
pp. 443-459 ◽  
Author(s):  
Alan Arroyo ◽  
Dan McQuillan ◽  
R. Bruce Richter ◽  
Gelasio Salazar
Keyword(s):  
Empty Triangles

scholarly journals On Edge-Disjoint Empty Triangles of Point Sets

2012 ◽  
pp. 83-100 ◽  
Author(s):  
Javier Cano ◽  
Luis F. Barba ◽  
Toshinori Sakai ◽  
Jorge Urrutia
Keyword(s):  
Point Sets ◽  
Edge Disjoint ◽  
Empty Triangles

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 Triangles in Good Drawings of the Complete Graph

2015 ◽  
Vol 31 (2) ◽  
pp. 335-345 ◽  
Author(s):  
Oswin Aichholzer ◽  
Thomas Hackl ◽  
Alexander Pilz ◽  
Pedro Ramos ◽  
Vera Sacristán ◽  
...  
Keyword(s):  
Complete Graph ◽  
Empty Triangles

scholarly journals Empty Triangles in Complete Topological Graphs

2015 ◽  
Vol 53 (4) ◽  
pp. 703-712
Author(s):  
Andres J. Ruiz-Vargas
Keyword(s):  
Topological Graphs ◽  
Empty Triangles

No Selection Lemma for Empty Triangles

2021 ◽  
pp. 720-725
Author(s):  
Ruy Fabila-Monroy ◽  
Carlos Hidalgo-Toscano ◽  
Daniel Perz ◽  
Birgit Vogtenhuber
Keyword(s):  
Empty Triangles ◽  
Selection Lemma

scholarly journals Counting Non-Convex 5-Holes in a Planar Point Set

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 78
Author(s):  
Young-Hun Sung ◽  
Sang Won Bae
Keyword(s):  
General Position ◽  
Brute Force ◽  
Expected Number ◽  
Planar Point ◽  
Point Set ◽  
Empty Triangles ◽  
Bounded Body

Let S be a set of n points in the general position, that is, no three points in S are collinear. A simple k-gon with all corners in S such that its interior avoids any point of S is called a k-hole. In this paper, we present the first algorithm that counts the number of non-convex 5-holes in S. To our best knowledge, prior to this work there was no known algorithm in the literature except a trivial brute force algorithm. Our algorithm runs in time O(T+Q), where T denotes the number of 3-holes, or empty triangles, in S and Q that denotes the number of non-convex 4-holes in S. Note that T+Q ranges from Ω(n2) to O(n3), while its expected number is Θ(n2logn) when the points in S are chosen uniformly and independently at random from a convex and bounded body in the plane.

scholarly journals Monochromatic empty triangles in two-colored point sets

2013 ◽  
Vol 161 (9) ◽  
pp. 1259-1261 ◽  
Author(s):  
János Pach ◽  
Géza Tóth
Keyword(s):  
Point Sets ◽  
Empty Triangles ◽  
Colored Point

On empty triangles determined by points in the plane

1988 ◽  
Vol 51 (3-4) ◽  
pp. 323-328 ◽  
Author(s):  
M. Katchalski ◽  
A. Meir
Keyword(s):  
Empty Triangles

CO2 photoconversion to fuels under high pressure: effect of TiO2 phase and of unconventional reaction conditions

2015 ◽  
Vol 5 (9) ◽  
pp. 4481-4487 ◽  
Author(s):  
I. Rossetti ◽  
A. Villa ◽  
M. Compagnoni ◽  
L. Prati ◽  
G. Ramis ◽  
...  
Keyword(s):  
High Pressure ◽  
Pressure Effect ◽  
Reaction Conditions ◽  
Empty Triangles ◽  
Tio2 Phase ◽  
Reactor Pressure ◽  
High Pressure Effect

Effect of CO2 saturation and reactor pressure on H2 (full triangles) and CH4 (circles) productivity at pH = 11.4, T = 65 °C. H2 productivity (empty triangles) at pH 5.5, T = 65 °C. Sample 0.1 wt% Au/P25.

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