TY - JOUR
T1 - A continuous characterization of the maximum vertex-weighted clique in hypergraphs
AU - Tang, Qingsong
AU - Zhang, Xiangde
AU - Wang, Guoren
AU - Zhao, Cheng
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - 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: max{ xTAx} on the standard simplex: {∑i=1nxi=1,xi≥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.
AB - 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: max{ xTAx} on the standard simplex: {∑i=1nxi=1,xi≥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.
KW - Cliques of hypergraphs
KW - Polynomial optimization
KW - Vertex-weighted hypergraphs
UR - https://www.scopus.com/pages/publications/85042447981
U2 - 10.1007/s10878-018-0259-9
DO - 10.1007/s10878-018-0259-9
M3 - Article
AN - SCOPUS:85042447981
SN - 1382-6905
VL - 35
SP - 1250
EP - 1260
JO - Journal of Combinatorial Optimization
JF - Journal of Combinatorial Optimization
IS - 4
ER -