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On hereditary properties of the class of graphs with convex quadratic stability number

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Abstract

We show that the class of graphs with quadratic stability number is not hereditary. Then we prove that this class contains a unique maximal hereditary subclass and, finally, we characterize this subclass by two forbidden induced subgraphs.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal

    D. M. Cardoso

  2. DIMAP and Mathematics Institute, University of Warwick, Coventry, UK

    V. V. Lozin

Authors
  1. D. M. Cardoso
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  2. V. V. Lozin
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Corresponding author

Correspondence to D. M. Cardoso.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 71, Algebraic Techniques in Graph Theory and Optimization, 2011.

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Cardoso, D.M., Lozin, V.V. On hereditary properties of the class of graphs with convex quadratic stability number. J Math Sci 182, 227–232 (2012). https://doi.org/10.1007/s10958-012-0743-1

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  • DOI: https://doi.org/10.1007/s10958-012-0743-1

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