On the Largest Graph-Lagrangian of 3-Graphs with Fixed Number of Edges

Yanping Sun (), Qingsong Tang (), Cheng Zhao () and Yuejian Peng ()
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Yanping Sun: Hunan University
Qingsong Tang: Northeastern University
Cheng Zhao: Indiana State University
Yuejian Peng: Hunan University

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 1, No 3, 57-79

Abstract: Abstract The Graph-Lagrangian of a hypergraph has been a useful tool in hypergraph extremal problems. In most applications, we need an upper bound for the Graph-Lagrangian of a hypergraph. Frankl and Füredi conjectured that the $${r}$$ r -graph with $$m$$ m edges formed by taking the first $$\textit{m}$$ m sets in the colex ordering of the collection of all subsets of $${\mathbb N}$$ N of size $${r}$$ r has the largest Graph-Lagrangian of all $$r$$ r -graphs with $$m$$ m edges. In this paper, we show that the largest Graph-Lagrangian of a class of left-compressed $$3$$ 3 -graphs with $$m$$ m edges is at most the Graph-Lagrangian of the $$\mathrm 3 $$ 3 -graph with $$m$$ m edges formed by taking the first $$m$$ m sets in the colex ordering of the collection of all subsets of $${\mathbb N}$$ N of size $${3}$$ 3 .

Keywords: Colex ordering; Left-compressed hypergraphs; Graph-Lagrangians of hypergraphs; Polynomial optimization; 05C35; 05C65; 65K10; 90C27; 94C15 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-013-0519-x

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