Hamiltonian Decompositions of Cayley Graphs on Abelian Groups of Odd Order

Alspach has conjectured that any 2k-regular connected Cayley graphcay(A, S) on a finite abelian groupAcan be decomposed intokhamiltonian cycles. In this paper, the conjecture is shown to be true ifS={s1,s2, …,sk} is a minimal generating set of an abelian groupAof odd order (where a generating setSof a groupGisminimalif no proper subset ofGcan generateG).