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
Feasible and infeasible maxima in a quadratic program for maximum clique
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
Continuous characterizations of the maximum clique problem
Mathematics of Operations Research
Annealed replication: a new heuristic for the maximum clique problem
Discrete Applied Mathematics
Exact bounds on the order of the maximum clique of a graph
Discrete Applied Mathematics
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A hypergraph extension of Turán's theorem
Journal of Combinatorial Theory Series B
Theoretical and algorithmic framework for hypergraph matching
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
Some results on Lagrangians of hypergraphs
Discrete Applied Mathematics
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In 1965 Motzkin and Straus established a remarkable connection between the local/global maximizers of the Lagrangian of a graph G over the standard simplex Δ and the maximal/maximum cliques of G . In this work we generalize the Motzkin-Straus theorem to k -uniform hypergraphs, establishing an isomorphism between local/global minimizers of a particular function over Δ and the maximal/maximum cliques of a k -uniform hypergraph. This theoretical result opens the door to a wide range of further both practical and theoretical applications, concerning continuous-based heuristics for the maximum clique problem on hypergraphs, as well as the discover of new bounds on the clique number of hypergraphs. Moreover we show how the continuous optimization task related to our theorem, can be easily locally solved by mean of a dynamical system.