Maximizing maximal angles for plane straight-line graphs

O. Aichholzer, T. Hackl, M. Hoffmann, C. Huemer, F. Santos, B. Speckmann, B. Vogtenhuber

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)


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 f-open if each vertex has an incident angle of size at least f. In this paper we study the following type of question: What is the maximum angle f 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 f-open? In particular, we consider the classes of triangulations, spanning trees, and spanning paths on S and give tight bounds in most cases.
Original languageEnglish
Pages (from-to)17-28
JournalComputational Geometry
Issue number1
Publication statusPublished - 2013


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