Before revision:  We analytically derive the criteria for which the reduction in the number of CNOT gates due to the DFS based technique can provide lower error probability even with some increased depth, and show that all graphs conform to this criteria, making this technique universal.
After revision:  We analytically derive the condition for which the reduction in the number of CNOT gates due to the DFS based technique can provide lower error probability even with some increased depth, and show that all graphs conform to this criteria, making this technique universal.