Matrix analysis
Spectral bounds for the clique and independence numbers of graphs
Journal of Combinatorial Theory Series B
Relaxation labeling networks for the maximum clique problem
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
Continuous characterizations of the maximum clique problem
Mathematics of Operations Research
Evolution towards the Maximum Clique
Journal of Global Optimization
Annealed replication: a new heuristic for the maximum clique problem
Discrete Applied Mathematics
A Continuous Characterization of Maximal Cliques in k-Uniform Hypergraphs
Learning and Intelligent Optimization
A new spectral bound on the clique number of graphs
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
On the maximum quasi-clique problem
Discrete Applied Mathematics
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The paper reviews some of the existing exact bounds to the maximum clique of a graph and successively presents a new upper and a new lower bound. The new upper bound is ω ≤ n - rank oA/2, where oA is the adjacency matrix of the complementary graph, and derives from a formulation of the maximum clique problem in complex space. The new lower bound is ω ≥ 1/(1 - gj*(α*)) (see text for details) and improves strictly the present best lower bound published by Wilf (J. Combin. Theory Ser. B 40 (1986) 113).Throughout the paper an eye is kept on the computational complexity of actually calculating the bounds. At the end, the various bounds are compared on 700 random graphs.