2013/02/26 by Munaro, Andrea
#Combinatorics (math.CO) #Computational Complexity (cs.CC) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1302.6500
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.