Browsing by Author "Huemer, Clemens"

3colorability of pseudotriangulations
Aichholzer, Oswin; Aurenhammer, Franz; Hackl, Thomas; Huemer, Clemens; Pilz, Alexander; Vogtenhuber, Birgit (2015)
Article
Open AccessDeciding 3colorability for general plane graphs is known to be an NPcomplete problem. However, for certain families of graphs, like triangulations, polynomial time algorithms exist. We consider the family of pseudotri ... 
4Holes in point sets
Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (20140801)
Article
Open AccessWe consider a variant of a question of Erdos on the number of empty kgons (kholes) in a set of n points in the plane, where we allow the kgons to be nonconvex. We show bounds and structural results on maximizing and ... 
4labelings and grid embeddings of plane quadrangulations
Barrière Figueroa, Eulalia; Huemer, Clemens (20090603)
External research report
Open AccessWe show that each quadrangulation on $n$ vertices has a closed rectangle of influence drawing on the $(n2) \times (n2)$ grid. Further, we present a simple algorithm to obtain a straightline drawing of a quadrangulation ... 
A new lower bound on the maximum number of plane graphs using production matrices
Huemer, Clemens; Pilz, Alexander; Silveira, Rodrigo Ignacio (2018)
Conference lecture
Restricted access  publisher's policyWe use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(41.77n) crossingfree geometric graphs. This improves the previously best known bound of ¿(41.18n) by Aichholzer ... 
Binary labelings for plane quadrangulations and their relatives
Felsner, Stefan; Huemer, Clemens; Kappes, Sarah; Orden, David (2010)
Article
Open AccessMotivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two ... 
Carathodory's theorem in depth
Fabila Monroy, Ruy; Huemer, Clemens (20170701)
Article
Open AccessLet X be a finite set of points in RdRd . The Tukey depth of a point q with respect to X is the minimum number tX(q)tX(q) of points of X in a halfspace containing q. In this paper we prove a depth version of Carathéodory’s ... 
Characteristic polynomials of production matrices for geometric graphs
Huemer, Clemens; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (20170801)
Article
Open AccessAn n×n production matrix for a class of geometric graphs has the property that the numbers of these geometric graphs on up to n vertices can be read off from the powers of the matrix. Recently, we obtained such production ... 
Compatible spanning trees
Garcia Olaverri, Alfredo Martin; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, Francisco Javier (20140701)
Article
Open AccessTwo plane geometric graphs are said to be compatible when their union is a plane geometric graph. Let S be a set of n points in the Euclidean plane in general position and let T be any given plane geometric spanning tree ... 
EdgeRemoval and NonCrossing Configurations in Geometric Graphs
Aichholzer, Oswin; Cabello, Sergio; Fabila Monroy, Ruy; Flores Peñaloza, David; Hackl, Thomas; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Wood, David (2010)
Article
Open AccessA geometric graph is a graph G = (V;E) drawn in the plane, such that V is a point set in general position and E is a set of straightline segments whose endpoints belong to V . We study the following extremal problem for ... 
Empty monochromatic simplices
Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Urrutia Galicia, Jorge (20140301)
Article
Open AccessLet S be a kcolored (finite) set of n points in , da parts per thousand yen3, in general position, that is, no (d+1) points of S lie in a common (d1)dimensional hyperplane. We count the number of empty monochromatic ... 
Empty nonconvex and convex fourgons in random point sets
Fabila Monroy, Ruy; Huemer, Clemens; Mitsche, Dieter (20150301)
Article
Open AccessLet S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A fourgon is called empty if it contains no points of S in its interior. We show that the expected number of empty ... 
Large bichromatic point sets admit empty monochromatic 4gons
Aichholzer, Oswin; Hackl, Thomas; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Vogtenhuber, Birgit (2009)
Conference report
Open AccessWe consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that ... 
Lower bounds for the number of small convex kholes
Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Pilz, Alexander; Vogtenhuber, Birgit (20140701)
Article
Open AccessLet S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdostype question on the least number h(k)(n) of convex kholes in S, and give improved lower bounds ... 
Lower bounds on the maximum number of noncrossing acyclic graphs
Huemer, Clemens; Mier Vinué, Anna de (20150801)
Article
Open AccessThis paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of noncrossing spanning trees and forests. We show that the socalled double chain ... 
Matching points with diametral disks
Huemer, Clemens; PérezLantero, Pablo; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (2017)
Conference report
Open AccessWe consider matchings between a set R of red points and a set B of blue points with diametral disks. In other words, for each pair of matched points p ¿ R and q ¿ B, we consider the diametral disk defined by p and q. We ... 
Maximizing maximal angles for plane straightline graphs
Aichholzer, Oswin; Hackl, Thomas; Hoffmann, Michael; Huemer, Clemens; Pór, Attila; Santos, Francisco; Speckmann, Bettina; Vogtenhuber, Birgit (201301)
Article
Restricted access  publisher's policyLet G=(S,E) be a plane straightline 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 of G that appear consecutively in the circular order ... 
Modem illumination of monotone polygons
Aichholzer, Oswin; Fabila Monroy, Ruy; Flores Peñaloza, David; Hackl, Thomas; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2009)
Conference report
Open AccessWe study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number k of walls. We call these ... 
Moving rectangles
García, Alfredo; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, F. Javier (2010)
Conference report
Open AccessConsider a set of n pairwise disjoint axisparallel rectangles in the plane. We call this set the source rectangles S. The aim is to move S to a set of (pairwise disjoint) target rectangles T . A move consists in a ... 
New results on production matrices for geometric graphs
Esteban Pascual, Guillermo; Huemer, Clemens; Silveira, Rodrigo Ignacio (20180701)
Article
Restricted access  publisher's policyWe present novel production matrices for noncrossing partitions, connected geometric graphs, and kangulations, which provide another way of counting the number of such objects. For instance, a formula for the number of ... 
Note on the number of obtuse angles in point sets
FabilaMonroy, Ruy; Huemer, Clemens; Tramuns, Eulàlia (201409)
Article
Open AccessIn $1979$ Conway, Croft, Erd\H{o}s and Guy proved that every set $S$ of $n$ points in general position in the plane determines at least $\frac{n^3}{18}O(n^2)$ obtuse angles and also presented a special set of $n$ points ...