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A continuous characterization of the maximum vertex-weighted clique in hypergraphs

Author

Listed:
  • Qingsong Tang

    (Northeastern University)

  • Xiangde Zhang

    (Northeastern University)

  • Guoren Wang

    (School of Computer Science and Engineering)

  • Cheng Zhao

    (Indiana State University)

Abstract

For a simple graph G on n vertices with adjacency matrix A, Motzkin and Strauss established a remarkable connection between the clique number and the global maximum value of the quadratic programm: $$\textit{max}\{ \mathbf {x}^T A \mathbf {x}\}$$ max { x T A x } on the standard simplex: $$\{\sum _{i=1}^{n} x_i =1, x_i \ge 0 \}$$ { ∑ i = 1 n x i = 1 , x i ≥ 0 } . In Gibbons et al. (Math Oper Res 122:754–768, 1997), an extension of the Motzkin–Straus formulation was provided for the vertex-weighted clique number of a graph. In this paper, we provide a continuous characterization of the maximum vertex-weighted clique problem for vertex-weighted uniform hypergraphs.

Suggested Citation

  • Qingsong Tang & Xiangde Zhang & Guoren Wang & Cheng Zhao, 2018. "A continuous characterization of the maximum vertex-weighted clique in hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1250-1260, May.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:4:d:10.1007_s10878-018-0259-9
    DOI: 10.1007/s10878-018-0259-9
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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.
    2. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, March.
    3. de Klerk, E. & Laurent, M. & Parrilo, P., 2006. "A PTAS for the minimization of polynomials of fixed degree over the simplex," Other publications TiSEM 603897c9-179e-43e4-9e83-6, Tilburg University, School of Economics and Management.
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