Now showing items 2-12 of 12

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

    Aichholzer, Oswin; Cardinal, Jean; Hackl, Thomas; Hurtado Díaz, Fernando Alfredo; Korman Cozzetti, Matias; 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 ...
  • Compatible matchings in geometric graphs 

    Aichholzer, Oswin; García Olaverri, Alfredo; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, F. Javier (Centre de Recerca Matemàtica, 2011)
    Conference report
    Open Access
    Two non-crossing geometric graphs on the same set of points are compatible if their union is also non-crossing. In this paper, we prove that every graph G that has an outerplanar embedding admits a non-crossing perfect ...
  • 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 ...
  • 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 ...
  • 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 ...
  • Two-convex polygons 

    Aichholzer, Oswin; Aurenhammer, Franz; Hurtado Díaz, Fernando Alfredo; Ramos, Pedro A.; Urrutia, J. (Université Libre de Bruxelles, 2009)
    Conference report
    Open Access
    We introduce a notion of k-convexity and explore some properties of polygons that have this property. In particular, 2-convex polygons can be recognized in O(n log n) time, and k-convex polygons can be triangulated in O(kn) time.