Hamilton Cycles that Extend Transposition Matchings in Cayley Graphs of Sn

Let B be a basis of transpositions for Sn and let Cay B Sn be the Cayley graph of Sn with respect to B It was shown by Kompel makher and Liskovets that Cay B Sn is hamiltonian We extend this result as follows Note that ev ery transposition b in B induces a perfect matchingMb in Cay B Sn We show here when n that for any b B there is a Hamilton cycle in Cay B Sn which includes every edge of Mb That is for n for any basis B of trans positions of Sn and for any b B it is possible to generate all permutations of n by transpositions in B so that every other transposition is b