Now showing items 1-20 of 46

    • 3-colorability of pseudo-triangulations 

      Aichholzer, Oswin; Aurenhammer, Franz; Hackl, Thomas; Huemer, Clemens; Pilz, Alexander; Vogtenhuber, Birgit (2015)
      Article
      Open Access
      Deciding 3-colorability for general plane graphs is known to be an NP-complete problem. However, for certain families of graphs, like triangulations, polynomial time algorithms exist. We consider the family of pseudo-tri ...
    • 4-Holes in point sets 

      Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2014-08-01)
      Article
      Open Access
      We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n points in the plane, where we allow the k-gons to be non-convex. We show bounds and structural results on maximizing and ...
    • 4-labelings and grid embeddings of plane quadrangulations 

      Barrière Figueroa, Eulalia; Huemer, Clemens (2009-06-03)
      External research report
      Open Access
      We show that each quadrangulation on $n$ vertices has a closed rectangle of influence drawing on the $(n-2) \times (n-2)$ grid. Further, we present a simple algorithm to obtain a straight-line 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 policy
      We use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(41.77n) crossing-free 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 (2019-11-01)
      Article
      Open Access
      We use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(42.11n ) crossing-free 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 Access
      Motivated 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 ...
    • CAL-A: Examen FQ: primavera 2019 

      Herranz Sotoca, Javier; Huemer, Clemens (Universitat Politècnica de Catalunya, 2019-06-07)
      Exam
      Restricted access to the UPC academic community
    • Carathodory's theorem in depth 

      Fabila Monroy, Ruy; Huemer, Clemens (2017-07-01)
      Article
      Open Access
      Let 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 (2017-08-01)
      Article
      Open Access
      An 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; Rubio-Montiel, Christian (2019-06-25)
      Article
      Open Access
      A decomposition of a non-empty simple graph G is a pair [G,P] such that P is a set of non-empty 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 (2014-07-01)
      Article
      Open Access
      Two 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, 2021-01-15)
      Exam
      Restricted access to the UPC academic community
    • DISCRETE AND ALGORITHMIC GEOMETRY | PARCIAL 

      Huemer, Clemens (Universitat Politècnica de Catalunya, 2019-10-31)
      Exam
      Restricted access to the UPC academic community
    • Edge-Removal and Non-Crossing 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 Access
      A 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 straight-line 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 (2014-03-01)
      Article
      Open Access
      Let S be a k-colored (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 (d-1)-dimensional hyperplane. We count the number of empty monochromatic ...
    • Empty non-convex and convex four-gons in random point sets 

      Fabila Monroy, Ruy; Huemer, Clemens; Mitsche, Dieter (2015-03-01)
      Article
      Open Access
      Let S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A four-gon 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 4-gons 

      Aichholzer, Oswin; Hackl, Thomas; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Vogtenhuber, Birgit (2009)
      Conference report
      Open Access
      We 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 k-holes 

      Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Pilz, Alexander; Vogtenhuber, Birgit (2014-07-01)
      Article
      Open Access
      Let 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 Erdos-type question on the least number h(k)(n) of convex k-holes in S, and give improved lower bounds ...
    • Lower bounds on the maximum number of non-crossing acyclic graphs 

      Huemer, Clemens; Mier Vinué, Anna de (2015-08-01)
      Article
      Open Access
      This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain ...
    • Matching points with diametral disks 

      Huemer, Clemens; Pérez-Lantero, Pablo; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (2017)
      Conference report
      Open Access
      We 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 ...