Un nouvel encadrement du nombre de cycle Hamiltoniens du n-cube. (New bounds for the number of Hamiltonian cycles of the n-cube) (Q1101468)

Let \(Q_ n\) be the n-cube, that is the graph where the nodes are words of length n on the alphabet \(\{\) 0,1\(\}\) and two vertices are linked by an edge if they differ in exactly one coordinate. Let h(n) be the number of Hamiltonian cycles of \(Q_ n\). For \(n\geq 5\) only bounds on h(n) are known. The author gives new upper and lower bounds for h(n).