Highly Influential

17 Excerpts

- Published 2013 in CTW

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.

@article{Munaro2013TheVO,
title={The VC-dimension of graphs with respect to k-connected subgraphs},
author={Andrea Munaro},
journal={Discrete Applied Mathematics},
year={2013},
volume={211},
pages={163-174}
}