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Are there any well studied graph theoretic properties that are common to all subgraphs of the boolean hypercubes that have a given VC dimension d.

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en.wikipedia.org/wiki/Bipartite_graph $\:$ –  Ricky Demer Aug 16 '12 at 19:26
    
@Ricky Demer Well,any induced subgraph of the boolean hypercube is bipartite. But the question is what other properties emerge when the set of boolean vectors that the nodes of the induced subgraph represent has VC dimension d? –  Arun Aug 17 '12 at 6:05

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