A generalization of the Motzkin–Straus theorem to hypergraphs

@article{Bul2009AGO,
  title={A generalization of the Motzkin–Straus theorem to hypergraphs},
  author={Samuel Rota Bul{\`o} and Marcello Pelillo},
  journal={Optimization Letters},
  year={2009},
  volume={3},
  pages={287-295}
}
In 1965, Motzkin and Straus established a remarkable connection between the global maxima of the Lagrangian of a graph G over the standard simplex and the clique number of G. In this paper, we provide a generalization of the Motzkin–Straus theorem to k-uniform hypergraphs (k-graphs). Specifically, given a k-graph G, we exhibit a family of (parameterized) homogeneous polynomials whose local (global) minimizers are shown to be in one-to-one correspondence with maximal (maximum) cliques of G. 

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