Abstract
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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Rota Bulò, S., Pelillo, M. A generalization of the Motzkin–Straus theorem to hypergraphs. Optim Lett 3, 287–295 (2009). https://doi.org/10.1007/s11590-008-0108-3
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DOI: https://doi.org/10.1007/s11590-008-0108-3