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Upper bounds on the independence and the clique covering number

  • Cyriel Van Nuffelen
  • Kristel Van Rompay
Article
  • 133 Downloads

Abstract.

New upper bounds for the independence number and for the clique covering number of a graph are given in terms of the rank, respectively the eigenvalues, of the adjacency matrix. We formulate a conjecture concerning an upper bound of the clique covering number. This upper bound is related to an old conjecture of Alan J. Hoffman which is shown to be false.

Key words: adjacency matrix, eigenvalues, independence number, clique covering number.

AMS classification: 05C.

Keywords

Adjacency Matrix Independence Number Covering Number Clique Covering Clique Covering Number 
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 2003

Authors and Affiliations

  1. 1.University of AntwerpAntwerpBelgium

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