The VC-Dimension of Graphs with Respect to k-Connected Subgraphs
Munaro, Andrea
Original · EN
We study the VC-dimension of the set system on the vertex set of some graph which is induced by the family of its k-connected subgraphs. In particular, we give tight upper and lower bounds for the VC-dimension. Moreover, we show that computing the VC-dimension is NP-complete and that it remains NP-complete for split graphs and for some subclasses of planar bipartite graphs in the cases k = 1 and k = 2. On the positive side, we observe it can be decided in linear time for graphs of bounded clique-width.
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