A continuous characterization of the maximum vertex-weighted clique in hypergraphs |
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Authors: | Qingsong Tang Xiangde Zhang Guoren Wang Cheng Zhao |
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Affiliation: | 1.College of Sciences,Northeastern University,Shenyang,People’s Republic of China;2.School of Computer Science and Engineering,Shenyang,People’s Republic of China;3.Department of Mathematics and Computer Science,Indiana State University,Terre Haute,USA |
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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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