Hamiltonian decompositions of Cayley graphs on Abelian groups

Abstract Alspach has conjectured that any 2k-regular connected Cayley graph cay(A,S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In this paper, the conjecture is shown to be true if S={s1,s2,s3} is a minimal generating set of A with |A| odd, or S={s1,s2,…,sk} is a generating set of A such that gcd(ord(si),ord(sj))= 1 for i≠j.