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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Acknowledgements
We thank the anonymous referee for helpful comments. This research is partially supported by Chinese Universities Scientific Fund (No. N140504004) and the Doctoral Starting up Foundation of Liaoning Province (No. 201601011).
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Tang, Q., Zhang, X., Wang, G. et al. A continuous characterization of the maximum vertex-weighted clique in hypergraphs. J Comb Optim 35, 1250–1260 (2018). https://doi.org/10.1007/s10878-018-0259-9
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DOI: https://doi.org/10.1007/s10878-018-0259-9