On the Complexity of Computing the k-restricted Edge-connectivity of a Graph

  • Luis Pedro Montejano
  • Ignasi SauEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)


The k -restricted edge-connectivity of a graph G, denoted by \(\lambda _k(G)\), is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least k vertices. This graph invariant, which can be seen as a generalization of a minimum edge-cut, has been extensively studied from a combinatorial point of view. However, very little is known about the complexity of computing \(\lambda _k(G)\). Very recently, in the parameterized complexity community the notion of good edge separation of a graph has been defined, which happens to be essentially the same as the k-restricted edge-connectivity. Motivated by the relevance of this invariant from both combinatorial and algorithmic points of view, in this article we initiate a systematic study of its computational complexity, with special emphasis on its parameterized complexity for several choices of the parameters. We provide a number of NP-hardness and W[1]-hardness results, as well as FPT-algorithms.


Graph cut k-restricted edge-connectivity Good edge separation Parameterized complexity FPT-algorithm polynomial kernel 

Supplementary material


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité de Montpellier 2MontpellierFrance
  2. 2.AlGCo project team, CNRS, LIRMMMontpellierFrance

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