Editing Eulerian path (section)

=== Special cases ===
An [[Asymptotic analysis|asymptotic formula]] for the number of Eulerian circuits in the [[complete graph]]s was determined by [[Brendan McKay (mathematician)|McKay]] and Robinson (1995):<ref>[[Brendan McKay (mathematician)|Brendan McKay]] and Robert W. Robinson, [http://cs.anu.edu.au/~bdm/papers/euler.pdf Asymptotic enumeration of eulerian circuits in the complete graph], ''[[Combinatorica]]'', 10 (1995), no. 4, 367–377.</ref>
:<math>
\operatorname{ec}(K_n) = 2^{\frac{(n+1)}{2}}\pi^{\frac{1}{2}} e^{\frac{-n^2}{2}+\frac{11}{12}} n^{\frac{(n-2)(n+1)}{2}} \bigl(1+O(n^{-\frac{1}{2}+\epsilon})\bigr).
</math>

A similar formula was later obtained by M.I. Isaev (2009) for [[complete bipartite graph]]s:<ref>{{cite journal |author=M.I. Isaev |title=Asymptotic number of Eulerian circuits in complete bipartite graphs |language=ru |journal=Proc. 52-nd MFTI Conference |year=2009 |place=Moscow |pages=111–114 }}</ref>
:<math>
\operatorname{ec}(K_{n,n}) = \left(\frac{n}{2}-1\right)!^{2n} 2^{n^2-n+\frac{1}{2}}\pi^{-n+\frac{1}{2}} n^{n-1}  \bigl(1+O(n^{-\frac{1}{2}+\epsilon})\bigr).
</math>