New Bounds on the Clique Number of Graphs Based on Spectral Hypergraph Theory

This work introduces new bounds on the clique number of graphs derived from a result due to S´os 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 a 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.

• Type: Conference
• Year: 2009
• Where: LION
• Authors: Samuel Rota Bulò, Marcello Pelillo
• Keywords: Clique Number, LION 2009, Optimization, Spectral Bounds, Spectral Hypergraph Theory