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Upper bounds on the independence and the clique covering number

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Quarterly Journal of the Belgian, French and Italian Operations Research Societies Aims and scope Submit manuscript

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.

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Authors and Affiliations

  1. University of Antwerp, Prinsstraat 13, 2000, Antwerp, Belgium

    Cyriel Van Nuffelen & Kristel Van Rompay

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  1. Cyriel Van Nuffelen
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  2. Kristel Van Rompay
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Correspondence to Cyriel Van Nuffelen.

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Nuffelen, C.V., Rompay, K.V. Upper bounds on the independence and the clique covering number. 4OR 1, 43–50 (2003). https://doi.org/10.1007/s10288-002-0002-2

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  • DOI: https://doi.org/10.1007/s10288-002-0002-2

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