The minimum chromatic spectrum of 3-uniform $$\mathcal{C}$$ -hypergraphs.

Let $$S(n,k)$$ be the Stirling number of the second kind. In this paper, we prove that for any integer $$n$$ at least three, there exists a 3-uniform $$\mathcal{C}$$ -hypergraph $$\mathcal{H}$$ with chromatic spectrum $$R(\mathcal{H})=(1,r_2,S(n,3),\ldots , S(n,n))$$ , which is the minimum chromatic spectrum of 3-uniform $$\mathcal{C}$$ -hypergraphs with upper chromatic number n. [ABSTRACT FROM AUTHOR]