  In order to consider j-wise relative r-primality conditions that do not
necessarily require all j-tuples of elements in a Dedekind domain to be
relatively r-prime, we define the notion of j-wise relative r-primality with
respect to a fixed j-uniform hypergraph H. This allows us to provide further
generalisations to several results on natural densities not only for a ring of
algebraic integers, but also for the ring F_q[x].
