Ara es mostren els items 1-20 de 28

  • 3-colorability of pseudo-triangulations 

    Aichholzer, Oswin; Aurenhammer, Franz; Hackl, Thomas; Huemer, Clemens; Pilz, Alexander; Vogtenhuber, Birgit (2015)
    Article
    Accés obert
    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
    Accés obert
    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)
    Report de recerca
    Accés obert
    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 ...
  • Binary labelings for plane quadrangulations and their relatives 

    Felsner, Stefan; Huemer, Clemens; Kappes, Sarah; Orden, David (2010)
    Article
    Accés obert
    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 ...
  • Compatible spanning trees 

    Garcia Olaverri, Alfredo Martin; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, Francisco Javier (2014-07-01)
    Article
    Accés obert
    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 ...
  • 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
    Accés obert
    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
    Accés obert
    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
    Accés obert
    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)
    Text en actes de congrés
    Accés obert
    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
    Accés obert
    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
    Accés obert
    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 ...
  • Maximizing maximal angles for plane straight-line graphs 

    Aichholzer, Oswin; Hackl, Thomas; Hoffmann, Michael; Huemer, Clemens; Pór, Attila; Santos, Francisco; Speckmann, Bettina; Vogtenhuber, Birgit (2013-01)
    Article
    Accés restringit per política de l'editorial
    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 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)
    Text en actes de congrés
    Accés obert
    We 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)
    Text en actes de congrés
    Accés obert
    Consider a set of n pairwise disjoint axis-parallel 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 ...
  • Note on the number of obtuse angles in point sets 

    Fabila-Monroy, Ruy; Huemer, Clemens; Tramuns, Eulàlia (2014-09)
    Article
    Accés obert
    In $1979$ 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 ...
  • On cyclic Kautz digraphs 

    Böhmová, Katerina; Dalfó Simó, Cristina; Huemer, Clemens (2015)
    Report de recerca
    Accés obert
    A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given ...
  • On k-gons and k-holes in point sets 

    Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Valtr, Pavel; Vogtenhuber, Birgit (2015-08-01)
    Article
    Accés obert
    We consider a variation of the classical Erdos-Szekeres problems on the existence and number of convex k-gons and k-holes (empty k-gons) in a set of n points in the plane. Allowing the k-gons to be non-convex, we show ...
  • On some partitioning problems for two-colored point sets 

    Grima, Clara; Hernando Martín, María del Carmen; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo (2009)
    Text en actes de congrés
    Accés obert
    Let S be a two-colored set of n points in general position in the plane. We show that S admits at least 2 n 17 pairwise disjoint monochromatic triangles with vertices in S and empty of points of S. We further show ...
  • On the disks with diameters the sides of a convex 5-gon 

    Huemer, Clemens; Pérez-Lantero, Pablo (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II (MA2), 2015)
    Text en actes de congrés
    Accés restringit per política de l'editorial
    We prove that for any convex pentagon there are two disks, among the five disks having a side of the pentagon as diameter and the midpoint of the side as its center, that do not intersect. This shows that K5 is never the ...
  • Production matrices for geometric graphs 

    Huemer, Clemens; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (2016)
    Article
    Accés restringit per política de l'editorial
    We present production matrices for non-crossing geometric graphs on point sets in convex position, which allow us to derive formulas for the numbers of such graphs. Several known identities for Catalan numbers, Ballot ...