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On Motzkin–Straus type results for non-uniform hypergraphs

Author

Listed:
  • Qingsong Tang

    (Northeastern University)

  • Yuejian Peng

    (Hunan University)

  • Xiangde Zhang

    (Northeastern University)

  • Cheng Zhao

    (Indiana State University)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:2:d:10.1007_s10878-016-0084-y
    DOI: 10.1007/s10878-016-0084-y
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Yuejian Peng & Qingsong Tang & Cheng Zhao, 2015. "On Lagrangians of r-uniform hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 812-825, October.
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