Reviews: Structure Learning with Side Information: Sample Complexity

Major comments: Throughout the paper k is used to refer to the maximum number of edges in a graph, but I'm unclear if that means that the proofs hold for some k max(k_1,k_2) where k_1 is the number of edges in G_1, etc, and k_1 and k_2 are allowed to be different. If it doesn't allow each graph to have a different value for k this should be made clear. If it does allow that, then it's unclear what ranges of k the proofs hold for (presumably min(k_1,k_2) is lower bounded by \gamma k). Allowing each graph to have a different k implies that there could be different recovery rates for each graph, but the error metric is over the full joint space (rather than the subgraph or independently in the two graphs). Is it possible to make statements about the error metric just in the shared subgraph?