  We discuss properties which must be satisfied by a genetic network in order
for it to allow differentiation.
  These conditions are expressed as follows in mathematical terms. Let $F$ be a
differentiable mapping from a finite dimensional real vector space to itself.
The signs of the entries of the Jacobian matrix of $F$ at a given point $a$
define an interaction graph, i.e. a finite oriented finite graph $G(a)$ where
each edge is equipped with a sign. Ren\'e Thomas conjectured twenty years ago
that, if $F$ has at least two non degenerate zeroes, there exists $a$ such that
$G(a)$ contains a positive circuit. Different authors proved this in special
cases, and we give here a general proof of the conjecture. In particular, we
get this way a necessary condition for genetic networks to lead to
multistationarity, and therefore to differentiation.
  We use for our proof the mathematical literature on global univalence, and we
show how to derive from it several variants of Thomas' rule, some of which had
been anticipated by Kaufman and Thomas.
