Finding Highly Connected Subgraphs

  • Falk Hüffner
  • Christian Komusiewicz
  • Manuel Sorge
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8939)


A popular way of formalizing clusters in networks are highly connected subgraphs, that is, subgraphs of k vertices that have edge connectivity larger than k/2 (equivalently, minimum degree larger than k/2). We examine the computational complexity of finding highly connected subgraphs. We first observe that this problem is NP-hard. Thus, we explore possible parameterizations, such as the solution size, number of vertices in the input, the size of a vertex cover in the input, and the number of edges outgoing from the solution (edge isolation), and expose their influence on the complexity of this problem. For some parameters, we find strong intractability results; among the parameters yielding tractability, the edge isolation seems to provide the best trade-off between running time bounds and a small parameter value in relevant instances.


Vertex Cover Reduction Rule Edge Deletion Problem Kernel Search Tree Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Falk Hüffner
    • 1
  • Christian Komusiewicz
    • 1
  • Manuel Sorge
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany

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