Hamilton decompositions of certain 6-regular Cayley graphs on Abelian groups with a cyclic subgroup of index two

Alspach conjectured that every connected Cayley graph of even valency on a finite Abelian group is Hamilton-decomposable. Using some techniques of Liu, this article shows that if AA is an Abelian group of even order with a generating set {a,b}{a,b}, and AA contains a subgroup of index two, generated by cc, then the 66-regular Cayley graph Cay(A;{a,b,c}⋆) is Hamilton-decomposable.