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

Ruixue Zhang, Ping Zhao, Kefeng Diao () and Fuliang Lu
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Ruixue Zhang: Linyi University
Ping Zhao: Linyi University
Kefeng Diao: Linyi University
Fuliang Lu: Linyi University

Journal of Combinatorial Optimization, 2015, vol. 29, issue 4, No 8, 796-802

Abstract: Abstract Let $$S(n,k)$$ S ( n , k ) be the Stirling number of the second kind. In this paper, we prove that for any integer $$n$$ n at least three, there exists a 3-uniform $$\mathcal{C}$$ C -hypergraph $$\mathcal{H}$$ H with chromatic spectrum $$R(\mathcal{H})=(1,r_2,S(n,3),\ldots , S(n,n))$$ R ( H ) = ( 1 , r 2 , S ( n , 3 ) , … , S ( n , n ) ) , which is the minimum chromatic spectrum of 3-uniform $$\mathcal{C}$$ C -hypergraphs with upper chromatic number n.

Keywords: $$\mathcal{C}$$ C -hypergraph; Chromatic spectrum; Stirling number of the second kind; 15A36 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-013-9625-9

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