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Some Motzkin–Straus type results for non-uniform hypergraphs

Author

Listed:
  • Ran Gu

    (Nankai University)

  • Xueliang Li

    (Nankai University)

  • Yuejian Peng

    (Hunan University)

  • Yongtang Shi

    (Nankai University)

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.

Suggested Citation

  • Ran Gu & Xueliang Li & Yuejian Peng & Yongtang Shi, 2016. "Some Motzkin–Straus type results for non-uniform hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 223-238, January.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:1:d:10.1007_s10878-014-9736-y
    DOI: 10.1007/s10878-014-9736-y
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    References listed on IDEAS

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    1. Luana E. Gibbons & Donald W. Hearn & Panos M. Pardalos & Motakuri V. Ramana, 1997. "Continuous Characterizations of the Maximum Clique Problem," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 754-768, August.
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    1. Qingsong Tang & Yuejian Peng & Xiangde Zhang & Cheng Zhao, 2017. "On Motzkin–Straus type results for non-uniform hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 504-521, August.

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