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Maximizing Maximal Angles for Plane Straight-Line Graphs

  • Oswin Aichholzer
  • Thomas Hackl
  • Michael Hoffmann
  • Clemens Huemer
  • Attila Pór
  • Francisco Santos
  • Bettina Speckmann
  • Birgit Vogtenhuber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4619)

Abstract

Let G = (S, E) be a plane straight-line graph on a finite point set Open image in new window 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 of the edges incident to p. A plane straight-line graph is called ϕ-open if each vertex has an incident angle of size at least ϕ. In this paper we study the following type of question: What is the maximum angle ϕ such that for any finite set Open image in new window of points in general position we can find a graph from a certain class of graphs on S that is ϕ-open? In particular, we consider the classes of triangulations, spanning trees, and paths on S and give tight bounds in most cases.

Keywords

Incident Angle Span Tree General Position Maximal Angle Vertex Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Oswin Aichholzer
    • 1
  • Thomas Hackl
    • 1
  • Michael Hoffmann
    • 2
  • Clemens Huemer
    • 3
  • Attila Pór
    • 4
  • Francisco Santos
    • 5
  • Bettina Speckmann
    • 6
  • Birgit Vogtenhuber
    • 1
  1. 1.Institute for Software Technology, Graz University of Technology 
  2. 2.Institute for Theoretical Computer Science, ETH Zürich 
  3. 3.Departament de Matemática Aplicada II, Universitat Politécnica de Catalunya 
  4. 4.Dept. of Appl. Mathem. and Inst. for Theoretical Comp. Science, Charles Univ. 
  5. 5.Dept. de Matemáticas, Estadística y Computación, Universidad de Cantabria 
  6. 6.Department of Mathematics and Computer Science, TU Eindhoven 

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