Abstract
For any set S of positive integers, a mixed hypergraph H is a one-realization of S if its feasible set is S 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 S and get the following results: each colorable mixed hypergraph can be embedded into a one-realization of S; there exist one-realizations of S which are C-perfect; furthermore, for any positive integer k, there exists a one-realization H of S with αC(H)−χ¯(H)>k.
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