Independence densities of hypergraphs
Combinatorics
2013-08-14 v1
Abstract
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.
Cite
@article{arxiv.1308.2837,
title = {Independence densities of hypergraphs},
author = {Anthony Bonato and Jason Brown and Dieter Mitsche and Pawel Pralat},
journal= {arXiv preprint arXiv:1308.2837},
year = {2013}
}