  The first part of Hilbert's sixteenth problem deals with the classification
of the isotopy types realizable by real plane algebraic curves of a given
degree $m$. For $m = 9$, the classification of the $M$-curves is still wide
open. Let $C_9$ be an $M$-curve of degree 9 and $O$ be a non-empty oval of
$C_9$. If $O$ contains in its interior $\alpha$ ovals that are all empty, we
say that $O$ together with these $\alpha$ ovals forms a nest. The present paper
deals with the $M$-curves with three nests. Let $\alpha_i, i = 1, 2, 3$ be the
numbers of empty ovals in each nest. We prove that at least one of the
$\alpha_i$ is odd. This is a step towards a conjecture of A. Korchagin,
claiming that at least two of the $\alpha_i$ should be odd.
