Browsing by Author "Huemer, Clemens"
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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 ... 
A new lower bound on the maximum number of plane graphs using production matrices
Huemer, Clemens; Pilz, Alexander; Silveira, Rodrigo Ignacio (20191101)
Article
Open AccessWe use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(42.11n ) 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 ... 
CALA: Examen FQ: primavera 2019
Herranz Sotoca, Javier; Huemer, Clemens (Universitat Politècnica de Catalunya, 20190607)
Exam
Restricted access to the UPC academic community 
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 ... 
Coloring decompositions of complete geometric graphs
Huemer, Clemens; Lara, Dolores; RubioMontiel, Christian (20190625)
Article
Open AccessA decomposition of a nonempty simple graph G is a pair [G,P] such that P is a set of nonempty induced subgraphs of G, and every edge of G belongs to exactly one subgraph in P. The chromatic index ¿'([G,P]) of a decomposition ... 
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 ... 
DISCRETE AND ALGORITHMIC GEOMETRY  PARCIAL
Huemer, Clemens (Universitat Politècnica de Catalunya, 20191031)
Exam
Restricted access to the UPC academic community 
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 ... 
Matching points with disks with a common intersection
Huemer, Clemens; Pérez Lantero, Pablo; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (20190701)
Article
Restricted access  publisher's policyWe consider matchings with diametral disks between two sets of points R and B. More precisely, for each pair of matched points p ¿ R and q ¿ B, we consider the disk through p and q with the smallest diameter. We prove that ...