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Published in:
01-05-2015
The minimum chromatic spectrum of 3-uniform \(\mathcal{C}\)-hypergraphs
Published in: Journal of Combinatorial Optimization | Issue 4/2015
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Abstract
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.