New bounds on the clique number of graphs based on spectral hypergraph theory

Abstract

This work introduces new bounds on the clique number of graphs derived from a result due to Sós and Straus, which generalizes the Motzkin-Straus Theorem to a specific class of hypergraphs. In particular, we generalize and improve the spectral bounds introduced by Wilf in 1967 and 1986 establishing an interesting link between the clique number and the emerging spectral hypergraph theory field. In order to compute the bounds we face the problem of extracting the leading H-eigenpair of supersymmetric tensors, which is still uncovered in the literature. To this end, we provide two approaches to serve the purpose. Finally, we present some preliminary experimental results. © 2009 Springer-Verlag.