  We consider events over the probability space generated by the degree
sequences of multiple independent Erd\H{o}s-R\'enyi random graphs, and consider
an approximation probability space where such degree sequences are deemed to be
sequences of i.i.d. random variables. We show that, for any sequence of events
with probabilities asymptotically smaller than some power law in the
approximation model, the same upper bound also holds in the original model. We
accomplish this by extending an approximation framework proposed in a seminal
paper by McKay and Wormald. Finally, as an example, we apply the developed
framework to bound the probability of isomorphism-related events over multiple
independent random graphs.
