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Título: | Maximizing maximal angles for plane straight-line graphs |
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Autor/a: | Aichholzer, Oswin; Hackl, Thomas; Hoffmann, Michael; Huemer, Clemens; Pór, Attila; Santos, Francisco; Speckmann, Bettina; Vogtenhuber, Birgit |
Otros autores: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
Abstract: | 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 spanning paths on S and give tight bounds in most cases. |
Abstract: | Peer Reviewed |
Materia(s): | -Àrees temàtiques de la UPC::Aeronàutica i espai -Geometry, Plane -Triangulation -Triangulació |
Derechos: | Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Tipo de documento: | Artículo - Versión publicada Artículo |
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