Agrawala, "Author's response to `On mutual exclusion in computer networks' by Carvalho and Roucairol

Abstract. In 1965 Motzkin and Straus established a remarkable con-nection between the local/global maximizers of the Lagrangian of a graph G over the standard simplex ∆ 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 minimiz-ers of a particular function over ∆ 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, con-cerning continuous-based heuristics for the maximum clique problem on hypergraphs, as well as the discover of new bounds on the clique num-ber 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.