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A continuous characterization of the maximum vertex-weighted clique in hypergraphs
Authors:Qingsong Tang  Xiangde Zhang  Guoren Wang  Cheng Zhao
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
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.
Keywords:
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