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)
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 ... 
Algorithmic geometry with infinite time computation
Huemer, Clemens; Muller, Moritz Martin; Seara Ojea, Carlos; Tobar Nicolau, Adrián (2021)
Conference report
Restricted access  publisher's policy 
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
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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
Huemer, Clemens (Universitat Politècnica de Catalunya, 20210115)
Exam
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DISCRETE AND ALGORITHMIC GEOMETRY  PARCIAL
Huemer, Clemens (Universitat Politècnica de Catalunya, 20191031)
Exam
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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 ... 
GEOMETRIA DISCRETA I ALGORÍTMICA  FINAL
Silveira, Rodrigo Ignacio; Huemer, Clemens; Pfeifle, Julián (Universitat Politècnica de Catalunya, 20231219)
Exam
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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 ...