Maximizing Maximal Angles for Plane Straight-Line Graphs

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 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 S ⊂ R2 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.

• Type: Conference
• Year: 2007
• Where: WADS
• Authors: Oswin Aichholzer, Thomas Hackl, Michael Hoffmann, Clemens Huemer, Attila Pór, Francisco Santos, Bettina Speckmann, Birgit Vogtenhuber
• Keywords: Algorithms, General Position, Incident Angle, Plane Straight-line Graph, WADS 2007