Independence densities of hypergraphs [article]

Anthony Bonato, Jason Brown, Dieter Mitsche, Pawel Pralat
2013 arXiv   pre-print
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
more » ... number in [0,1]. Finally, we extend the notion of independence density via independence polynomials.
arXiv:1308.2837v1 fatcat:cidyv45qejgwtbugpkrkn5id2e