The VC-dimension of graphs with respect to k-connected subgraphs

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We study the VC-dimension of the set system on the vertex set of some graph which is induced by the family of its -connected subgraphs. In particular, we give tight upper and lower bounds for the VC-dimension. Moreover, we show that computing the VC-dimension is -complete and that it remains -complete for split graphs and for some subclasses of planar bipartite graphs in the cases and . On the positive side, we observe it can be decided in linear time for graphs of bounded clique-width.
Original languageEnglish
Pages (from-to)163-174
Number of pages12
JournalDiscrete Applied Mathematics
Publication statusPublished - 01 Oct 2016


  • NP-complete
  • VC-dimension
  • k-connected

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