4 research outputs found
Independence densities of hypergraphs
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 -free densities of graphs for a given graph
In the case of -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 Finally,
we extend the notion of independence density via independence polynomials