The smallest one-realization of a given set IV

Let SS be a finite set of positive integers. A mixed hypergraph HH is a one-realization of SS if its feasible set is SS and each entry of its chromatic spectrum is either 0 or 1. In Zhao et al. (2012), we determined the minimum number of vertices of a 3-uniform bi-hypergraph which is a one-realization of SS. In this paper, we generalize this result to rr-uniform bi-hypergraphs.