Some Motzkin–Straus type results for non-uniform hypergraphs

Ran Gu (), Xueliang Li (), Yuejian Peng () and Yongtang Shi ()
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Ran Gu: Nankai University
Xueliang Li: Nankai University
Yuejian Peng: Hunan University
Yongtang Shi: Nankai University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 1, No 16, 223-238

Abstract: Abstract A remarkable connection between the order of a maximum clique and the Lagrangian of a graph was established by Motzkin and Straus in 1965. This connection and its extensions were applied in Turán problems of graphs and uniform hypergraphs. Very recently, the study of Turán densities of non-uniform hypergraphs has been motivated by extremal poset problems. Peng et al. showed a generalization of Motzkin–Straus result for $$\{1,2\}$$ { 1 , 2 } -graphs. In this paper, we attempt to explore the relationship between the Lagrangian of a non-uniform hypergraph and the order of its maximum cliques. We give a Motzkin–Straus type result for $$\{1,r\}$$ { 1 , r } -graphs. Moreover, we also give an extension of Motzkin–Straus theorem for $$\{1, r_2, \cdots , r_l\}$$ { 1 , r 2 , ⋯ , r l } -graphs.

Keywords: Lagrangians of hypergraphs; Turán problems; extremal problems; 05C65; 05D05 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-014-9736-y

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