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

Qingsong Tang (), Xiangde Zhang (), Guoren Wang () and Cheng Zhao ()
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Qingsong Tang: Northeastern University
Xiangde Zhang: Northeastern University
Guoren Wang: School of Computer Science and Engineering
Cheng Zhao: Indiana State University

Journal of Combinatorial Optimization, 2018, vol. 35, issue 4, No 13, 1250-1260

Abstract: 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.

Keywords: Vertex-weighted hypergraphs; Cliques of hypergraphs; Polynomial optimization; 90C27; 05C65 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-018-0259-9

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