Hamiltonian decompositions of Cayley graphs on Abelian groups of odd order

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 = {s(1), s(2), ..., s(k)} is a minimal generating set of an abelian group A of odd order (where a generating set S of a group G is minimal if no proper subset of S can generate G). (C) 1996 Academic Press, Inc.