On perfection and imperfection of one-realizations of a given set

For any set SS 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 this paper, we focus on several special kinds of one-realizations of a given set SS and get the following results: each colorable mixed hypergraph can be embedded into a one-realization of SS; there exist one-realizations of SS which are CC-perfect; furthermore, for any positive integer kk, there exists a one-realization HH of SS with αC(H)−χ¯(H)>k.