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.
chromatic spectrum \(\mathcal{c}\)-hypergraph stirling number of the second kind 15a36