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A Magnetic Procedure for the Stability Number

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Abstract

A magnet is a pair u, v of adjacent vertices such that the proper neighbours of u are completely linked to the proper neighbours of v. It has been shown that one can reduce the graph by removing the two vertices u, v of a magnet and introducing a new vertex linked to all common neighbours of u and v without changing the stability number. We prove that all graphs containing no chordless cycle C k (k ≥ 5) and none of eleven forbidden subgraphs can be reduced to a stable set by repeated use of magnets. For such graphs a polynomial algorithm is given to determine the stability number.

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Authors and Affiliations

  1. École Polytechnique de Montréal and GERAD, Montreal, Canada

    Alain Hertz

  2. École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Dominique de Werra

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  1. Alain Hertz
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  2. Dominique de Werra
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Correspondence to Alain Hertz.

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Hertz, A., de Werra, D. A Magnetic Procedure for the Stability Number. Graphs and Combinatorics 25, 707–716 (2009). https://doi.org/10.1007/s00373-010-0886-0

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  • DOI: https://doi.org/10.1007/s00373-010-0886-0

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