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Journal of Combinatorial Optimization

, Volume 35, Issue 4, pp 1250–1260 | Cite as

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

  • Qingsong Tang
  • Xiangde Zhang
  • Guoren Wang
  • Cheng Zhao
Article
  • 83 Downloads

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: \(\textit{max}\{ \mathbf {x}^T A \mathbf {x}\}\) on the standard simplex: \(\{\sum _{i=1}^{n} x_i =1, x_i \ge 0 \}\). 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.

Keywords

Vertex-weighted hypergraphs Cliques of hypergraphs Polynomial optimization 

Mathematics Subject Classification

90C27 05C65 

Notes

Acknowledgements

We thank the anonymous referee for helpful comments. This research is partially supported by Chinese Universities Scientific Fund (No. N140504004) and the Doctoral Starting up Foundation of Liaoning Province (No. 201601011).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Qingsong Tang
    • 1
  • Xiangde Zhang
    • 1
  • Guoren Wang
    • 2
  • Cheng Zhao
    • 3
  1. 1.College of SciencesNortheastern UniversityShenyangPeople’s Republic of China
  2. 2.School of Computer Science and EngineeringShenyangPeople’s Republic of China
  3. 3.Department of Mathematics and Computer ScienceIndiana State UniversityTerre HauteUSA

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