Now showing items 1-5 of 5

  • A polynomial bound for untangling geometric planar graphs 

    Bose, Prosenjit; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Langerman, Stefan; Morin, Pat; Wood, David (2009-12)
    Article
    Open Access
    To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos (Discrete Comput. Geom. 28(4): 585–592, 2002) asked if every n-vertex geometric planar ...
  • 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 ...
  • Every large point set contains many collinear points or an empty pentagon 

    Wood, David; Por, Attila; Abel, Zachary; Ballinger, Brad; Bose, Prosenjit; Collette, Sébastien; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Kominers, Scott Duke; Langerman, Stefan (2011-01)
    Article
    Restricted access - publisher's policy
    We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next ...
  • Extremal graph theory for metric dimension and diameter 

    Hernando Martín, María del Carmen; Mora Giné, Mercè; Seara Ojea, Carlos; Wood, David (2010-02-22)
    Article
    Open Access
    A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let ...
  • Extremal graph theory for metric dimension and diameter 

    Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Seara Ojea, Carlos; Wood, David (2010)
    Article
    Open Access