One-inclusion hypergraph density revisited

Authors:
Hans Ulrich Simon;Balázs Szörényi
Affiliations:
Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany;Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany and Hungarian Academy of Sciences and University of Szeged, Research Group on Artificial Intelligence, H-6720 ...
Venue:
Information Processing Letters
Year:
2010

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Abstract

In this paper, we show that the density of the one-inclusion hypergraph induced by a family of multi-valued functions is bounded by the pseudo-dimension of this family. (The original proof for this fact, that has been published quite recently, makes use of a wrong claim.) We show furthermore that the well-known graph-dimension is another upper bound on the density (which solves an open problem from Rubinstein et al. (2009) [4]).