Minimum d-blockers and d-transversals in graphs

  • Authors:
  • Marie-Christine Costa;Dominique Werra;Christophe Picouleau

  • Affiliations:
  • Ecole Nationale Supérieure des Techniques Avancées-Paristech and CEDRIC Laboratory, Paris, France;Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland;Conservatoire National des Arts et Métiers, CEDRIC Laboratory, Paris, France

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2011

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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 驴. 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.