On Motzkin–Straus type results for non-uniform hypergraphs

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

Journal of Combinatorial Optimization, 2017, vol. 34, issue 2, No 14, 504-521

Abstract: Abstract Recently, some extensions of Motzkin–Straus theorems were proved for non-uniform hypergraphs whose edges contain 1 or r vertices in Gu et al. (J Comb Optim 31:223–238, 2016), Peng et al. (Discret Appl Math 200:170–175, 2016a), where r is a given integer. It would be interesting if similar results hold for other non-uniform hypergraphs. In this paper, we establish some Motzkin–Straus type results for general non-uniform hypergraphs. In particular, we obtain some Motzkin–Straus type results in terms of the Lagrangian of non-uniform hypergraphs when there exist some edges consisting of 2 vertices in the given hypergraphs. The presented results unify some known Motzkin–Straus type results for both uniform and non-uniform hypergraphs and also provide solutions to a class of polynomial optimization problems over the standard simplex in Euclidean space.

Keywords: Cliques of hypergraphs; Lagrangians of hypergraphs; Polynomial optimization; 05C35; 05C65; 05D99; 90C27 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0084-y

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