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.
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Acknowledgments
The research is supported by NSF of China (No. 11226288) and NSF of Shandong Province (No. ZR2009AM013).
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Zhang, R., Zhao, P., Diao, K. et al. The minimum chromatic spectrum of 3-uniform \(\mathcal{C}\)-hypergraphs. J Comb Optim 29, 796–802 (2015). https://doi.org/10.1007/s10878-013-9625-9
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DOI: https://doi.org/10.1007/s10878-013-9625-9