Abstract
For any set S of positive integers, a mixed hypergraph $${\mathcal {H}}$$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, a tight lower bound on the minimum number of edges of 3-uniform bi-hypergraphs which are one-realizations of a given set S is presented. As a result, we partially solve an open problem proposed by Bujtas and Tuza in 2008.
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