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 A is an Abelian group of even order with a generating set { a , b } , and A contains a subgroup of index two, generated by c , then the 6 -regular Cayley graph Cay ( A ; { a , b , c } ⋆ ) is Hamilton-decomposable.