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EJC
2008
9 years 5 months ago
A simple proof for open cups and caps
Let X be a set of points in general position in the plane. General position means that no three points lie on a line and no two points have the same x-coordinate. Y X is a cup, r...
Jakub Cerný
DCG
2010
93views more  DCG 2010»
9 years 5 months ago
The Number of Generalized Balanced Lines
Let S be a set of r red points and b = r +2 blue points in general position in the plane. A line determined by them is said to be balanced if in each open half-plane bounded by th...
David Orden, Pedro Ramos, Gelasio Salazar
DCG
2010
57views more  DCG 2010»
9 years 5 months ago
Iterated Point-Line Configurations Grow Doubly-Exponentially
Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and ...
Joshua Cooper, Mark Walters
CCCG
2001
9 years 7 months ago
Tight degree bounds for pseudo-triangulations of points
We show that every set of n points in general position has a minimum pseudo-triangulation whose maximum vertex degree is five. In addition, we demonstrate that every point set in ...
Lutz Kettner, David G. Kirkpatrick, Bettina Speckm...
CCCG
2008
9 years 7 months ago
On distinct distances among points in general position and other related problems
A set of points in the plane is said to be in general position if no three of them are collinear and no four of them are cocircular. If a point set determines only distinct vector...
Adrian Dumitrescu
CCCG
2010
9 years 7 months ago
Triangulations with many points of even degree
Let S be a set of points in the plane in general position. A triangulation of S will be called even if all the points of S have an even degree. We show how to construct a triangul...
Jorge Urrutia, Canek Peláez, Adriana Ram&ia...
COMPGEOM
2010
ACM
9 years 10 months ago
Points with large quadrant-depth
We characterize the set of all pairs (a, b) such that for every set P of n points in general position in R2 there always exists a point p ∈ P and two opposite quadrants determin...
Roel Apfelbaum, Itay Ben-Dan, Stefan Felsner, Rom ...
WADS
2007
Springer
106views Algorithms» more  WADS 2007»
9 years 11 months ago
Maximizing Maximal Angles for Plane Straight-Line Graphs
Let G = (S, E) be a plane straight-line graph on a finite point set S ⊂ R2 in general position. The incident angles of a point p ∈ S in G are the angles between any two edges ...
Oswin Aichholzer, Thomas Hackl, Michael Hoffmann, ...
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