New results on lower bounds for the number of (≤k)-facets

Authors:
Oswin Aichholzer;Jesús García;David Orden;Pedro Ramos
Affiliations:
Institute for Software Technology, Graz University of Technology, Graz, Austria;Escuela Universitaria de Informática, Universidad Politécnica de Madrid, Madrid, Spain;Departamento de Matemáticas, Universidad de Alcalá, Alcalá de Henares, Spain;Departamento de Matemáticas, Universidad de Alcalá, Alcalá de Henares, Spain
Venue:
European Journal of Combinatorics
Year:
2009

Citing 4
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GD'04 Proceedings of the 12th international conference on Graph Drawing

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Abstract

In this paper we present two different results dealing with the number of (@?k)-facets of a set of points: 1.We give structural properties of sets in the plane that achieve the optimal lower bound 3(k+22) of (@?k)-edges for a fixed 0@?k@?@?n/3@?-1; and 2.we show that, for k