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

  • Samuel Rota Bulò
  • Marcello Pelillo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5851)

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.

Keywords

Random Graph Undirected Graph Spectral Radius Maximum Clique Generalize Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Samuel Rota Bulò
    • 1
  • Marcello Pelillo
    • 1
  1. 1.Dipartimento di InformaticaUniversità Ca’ Foscari di VeneziaVeniceItaly

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