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Minimum d-blockers and d-transversals in graphs

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Abstract

We consider a set V of elements and an optimization problem on V: the search for a maximum (or minimum) cardinality subset of V verifying a given property ℘. A d-transversal is a subset of V which intersects any optimum solution in at least d elements while a d-blocker is a subset of V whose removal deteriorates the value of an optimum solution by at least d. We present some general characteristics of these problems, we review some situations which have been studied (matchings, s–t paths and s–t cuts in graphs) and we study d-transversals and d-blockers of stable sets or vertex covers in bipartite and in split graphs.

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Authors and Affiliations

  1. Ecole Nationale Supérieure des Techniques Avancées-Paristech and CEDRIC Laboratory, Paris, France

    Marie-Christine Costa

  2. Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Dominique de Werra

  3. Conservatoire National des Arts et Métiers, CEDRIC Laboratory, Paris, France

    Christophe Picouleau

Authors
  1. Marie-Christine Costa
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  2. Dominique de Werra
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  3. Christophe Picouleau
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Corresponding author

Correspondence to Christophe Picouleau.

Additional information

The first version of this paper was completed on January 21, 2010 for the 168th anniversary of the birth of Alferd Packer to whom it is dedicated.

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Costa, MC., de Werra, D. & Picouleau, C. Minimum d-blockers and d-transversals in graphs. J Comb Optim 22, 857–872 (2011). https://doi.org/10.1007/s10878-010-9334-6

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  • DOI: https://doi.org/10.1007/s10878-010-9334-6

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