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 hamiltonia n 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.