# Maximizing Maximal Angles for Plane Straight-Line Graphs - Computer Science > Computational Geometry

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Abstract: Let $G=(S, E)$ be a plane straight-line graph on a finite point set$S\subset\R^2$ in general position. The incident angles of a vertex $p \in S$of $G$ are the angles between any two edges of $G$ that appear consecutively inthe circular order of the edges incident to $p$.A plane straight-line graph is called $\phi$-open if each vertex has anincident angle of size at least $\phi$. In this paper we study the followingtype of question: What is the maximum angle $\phi$ such that for any finite set$S\subset\R^2$ of points in general position we can find a graph from a certainclass of graphs on $S$ that is $\phi$-open? In particular, we consider theclasses of triangulations, spanning trees, and paths on $S$ and give tightbounds in most cases.

Author: ** Oswin Aichholzer, Thomas Hackl, Michael Hoffmann, Clemens Huemer, Attila Por, Francisco Santos, Bettina Speckmann, Birgit Vogtenhuber**

Source: https://arxiv.org/