Now showing items 1-11 of 11

    • 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 ...
    • Cell-paths in mono- and bichromatic line arrangements in the plane 

      Aichholzer, Oswin; Cardinal, Jean; Hackl, Thomas; Hurtado Díaz, Fernando Alfredo; Korman Cozzetti, Matías; Pilz, Alexander; Silveira, Rodrigo Ignacio; Uehara, Ryuhei; Vogtenhuber, Birgit; Welzl, Emo (2014)
      Conference report
      Open Access
      We show that in every arrangement of n red and blue lines | in general position and not all of the same color | there is a path through a linear number of cells where red and blue lines are crossed alternatingly (and no ...
    • Empty triangles in good drawings of the complete graph 

      Aichholzer, Oswin; Hackl, Thomas; Pilz, Alexander; Ramos Alonso, Pedro Antonio; Sacristán Adinolfi, Vera; Vogtenhuber, Birgit (2015)
      Article
      Open Access
      A good drawing of a simple graph is a drawing on the sphere or, equivalently, in the plane in which vertices are drawn as distinct points, edges are drawn as Jordan arcs connecting their end vertices, and any pair of edges ...
    • Geodesic order types 

      Aichholzer, Oswin; Korman Cozzetti, Matías; Pilz, Alexander; Vogtenhuber, Birgit (2014-09-01)
      Article
      Restricted access - publisher's policy
      The geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained ...
    • 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 ...
    • 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
      Restricted access - publisher's policy
      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)
      Conference report
      Open Access
      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 ...
    • 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
      Open Access
      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 ...
    • Order types and cross-sections of line arrangements in R^3 

      Aichholzer, Oswin; Fabila-Monroy, Ruy; Hurtado Díaz, Fernando Alfredo; Pérez Lantero, Pablo; Ruiz Vargas, Andrés; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2014)
      Conference report
      Restricted access - publisher's policy
      We consider sets L = {l1,...., ln} of n labeled lines in general position in R3, and study the order types of point sets fp1; : : : ; png that stem from the intersections of the lines in L with (directed) planes II, not ...