One conjecture of bubble-sort graphs

The bubble-sort graph is an important interconnection network designed from Cayley graph model. One conjecture is proposed in Shi and Lu (2008) [10] as follows: for any integer n?2, if n is odd then bubble-sort graph Bn is a union of edge-disjoint hamiltonian cycles; if n is even then bubble-sort graph Bn is a union of edge-disjoint hamiltonian cycles and its perfect matching that has no edges in common with the hamiltonian cycles. In this paper, we prove that conjecture is true for n=5,6.