Consider the set of $r$-regular labeled graphs with $n$ vertices. There are results on its asymptotic size (see for instance this question on MO).

Is there a known, explicit lower bound on that size, valid for any $r$ and $n$?

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    $\begingroup$ It is easy to see that once you have your $N(r, n_0)=a>1,$ then $N(r, k n_0) \geq a^k.$ $\endgroup$ – Igor Rivin Mar 20 '17 at 16:37

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