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Article Dans Une Revue European Journal of Combinatorics Année : 2014

Independence densities of hypergraphs

Résumé

We consider the number of independent sets in hypergraphs, which allows us to define the independence density of countable hypergraphs. Hypergraph independence densities include a broad family of densities over graphs and relational structures, such as F-free densities of graphs for a given graph F. In the case of k-uniform hypergraphs, we prove that the independence density is always rational. In the case of finite but unbounded hyperedges, we show that the independence density can be any real number in [0, 1]. Finally, we extend the notion of independence density via independence polynomials.
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Dates et versions

hal-01143655 , version 1 (19-04-2015)

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Anthony Bonato, Jason Brown, Dieter Mitsche, Pawel Pralat. Independence densities of hypergraphs. European Journal of Combinatorics, 2014, 40, pp.124--136. ⟨10.1016/j.ejc.2014.03.001⟩. ⟨hal-01143655⟩
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