Journal of Combinatorial Optimization

, Volume 22, Issue 4, pp 857–872 | Cite as

Minimum d-blockers and d-transversals in graphs

  • Marie-Christine Costa
  • Dominique de Werra
  • Christophe Picouleau
Article

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, st paths and st cuts in graphs) and we study d-transversals and d-blockers of stable sets or vertex covers in bipartite and in split graphs.

Keywords

Transversal Blocker Cover Bipartite graph Split graph st path st cut Stable set Bilevel programming 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Marie-Christine Costa
    • 1
  • Dominique de Werra
    • 2
  • Christophe Picouleau
    • 3
  1. 1.Ecole Nationale Supérieure des Techniques Avancées-Paristech and CEDRIC LaboratoryParisFrance
  2. 2.Ecole Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.Conservatoire National des Arts et Métiers, CEDRIC LaboratoryParisFrance

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