Independence densities of hypergraphs

Anthony Bonato, Jason I. Brown, Dieter Mitsche, Paweł Prałat
2014 European journal of combinatorics (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 kuniform 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
more » ... number in [0, 1]. Finally, we extend the notion of independence density via independence polynomials.
doi:10.1016/j.ejc.2014.03.001 fatcat:ecnbwhb75ne45mn3dke5icesxa