2,811 research outputs found
Infinite hypergraphs I. Basic properties
AbstractBasic properties of the category of infinite directed hyperedge-labelled hypergraphs are studied. An algebraic structure is given which enables us to describe such hypergraphs by means of infinite expressions. It is then shown that two expressions define the same hypergraphs if and only if they are congruent with respect to some rewriting system. These results will be used in the second part of this paper to solve systems of recursive equations on hypergraphs and characterize their solutions
On structures in hypergraphs of models of a theory
We define and study structural properties of hypergraphs of models of a
theory including lattice ones. Characterizations for the lattice properties of
hypergraphs of models of a theory, as well as for structures on sets of
isomorphism types of models of a theory, are given
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
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