The answer is indeed positive. We furthermore have the following strongest
result.
\begin{thrm}
-There exist $b \in \Nats$ such that $\Gamma_{\{b\}}(f)$ is complete.
+There exists $b \in \Nats$ such that $\Gamma_{\{b\}}(f)$ is complete.
\end{thrm}
\begin{proof}
There is an arc $(x,y)$ in the
$\mathsf{N}$-cube.
In such a context, the Hamiltonian cycle is equivalent to a Gray code.
Many approaches have been proposed a way to build such codes, for instance
-the Reflected Binary Code. In this one, one of the bits is switched
-exactly $2^{\mathsf{N}-}$ \ANNOT{formule incomplète : $2^{\mathsf{N}-1}$ ??} for a $\mathsf{N}$-length cycle.
-
-%%%%%%%%%%%%%%%%%%%%%
-
-The function that is built
-from the \ANNOT{Phrase non terminée}
+the Reflected Binary Code. In this one and
+for a $\mathsf{N}$-length cycle, one of the bits is exactly switched
+$2^{\mathsf{N}-1}$ times whereas the others bits are modified at most
+$\left\lfloor \dfrac{2^{\mathsf{N-1}}}{\mathsf{N}-1} \right\rfloor$ times.
+It is clear that the function that is built from such a code would
+not provide a uniform output.
The next section presents how to build balanced Hamiltonian cycles in the
$\mathsf{N}$-cube with the objective to embed them into the
