\begin{theorem}
The Markov Matrix $M$ resulting from the $n$-cube in
which an Hamiltonian 
cycle is removed, is doubly stochastic.
\end{theorem}

\begin{theorem}
The iteration graph issued from the $n$-cube where an Hamiltonian 
cycle is removed is strongly connected.
\end{theorem}


\begin{block}{We are then left}
\begin{itemize}
\item To focus on the generation of Hamiltonian cycles in the 
$n$-cube, \textit{i.e.},
\item To find cyclic Gray codes: 
      sequences of $2^n$ codewords ($n$-bits strings) 
      where two successive elements differ in only one bit position and
      and where the last codeword   
      differs in only one bit position from the first one.