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.
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