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New Results in the Theory of Packing and Covering

  • Chapter
Convexity and Its Applications

Abstract

Let J be a system of sets. If all members of J are contained in a given set C and each point of C belongs to at most one member of J then J is said to be a packing into C. If, on the other hand, each point of C belongs to at least one member of J then we say that J is a covering of C. Packings and coverings have been considered in various spaces and on various combinatorial structures. Here we are interested in problems concerning packings and coverings consisting of convex bodies in spaces of constant curvature, i.e. in Euclidean, spherical and hyperbolic space. Instead of saying that J is a packing into the whole space or J is a covering of the whole space we shall simply use the terms J is a packing and J is a covering.

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  1. Mathematical Institute, Hungarian Academy of Sciences, Realtanoda u. 13-15, P. Box 428, H-1395, Budapest, Hungary

    G. Fejes Tóth

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  1. Institut für Analysis, Technische Mathematik und Versicherungsmathematik, Technische Universität Wien, Gusshausstrasse 25-27, A-1040, Wien, Austria

    Peter M. Gruber

  2. Lehrstuhl für Mathematik II, Universität Siegen, Hölderlinstrasse 3, D-5900, Siegen 21, Germany

    Jörg M. Wills

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Tóth, G.F. (1983). New Results in the Theory of Packing and Covering. In: Gruber, P.M., Wills, J.M. (eds) Convexity and Its Applications. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5858-8_14

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