** The number of trees half of whose vertices are leaves
and asymptotic enumeration of plane real algebraic curves
**

by V.M.~Kharlamov and S.Yu. Orevkov

__Abstract.__
The number of topologically different
plane real algebraic curves of a given degree *d*
has the form
exp(*C d*² +
*o*(*d*²)).
We determine the best available upper
bound for the constant *C*.
This bound follows from Arnold inequalities on the number of empty ovals.
To evaluate its rate we show its equivalence with the rate of growth
of the number of trees half of whose vertices are leaves and
evaluate the latter rate.