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

摘要

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,cblack star) is Hamilton-decomposable.