Ara es mostren els items 1-20 de 30

  • 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 ...
  • Carathodory's theorem in depth 

    Fabila Monroy, Ruy; Huemer, Clemens (2017-07-01)
    Article
    Accés restringit per política de l'editorial
    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
    Accés restringit per política de l'editorial
    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 ...
  • 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 ...