| Maximizing Maximal Angles for Plane Straight-Line Graphs ⋆ (2009) | |||||||||||||||
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| Abstract. Let G =(S, E) be a plane straight-line graph on a finite point set S ⊂ R 2 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 ⊂ R 2 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. 1 | |||||||||||||||
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