Abstract
Alspach has conjectured that any 2 k-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 3} is a minimal generating set of A with | A| odd, or S={ s 1, s 2,…, s k } is a generating set of A such that gcd( ord( s i ), ord( s j ))= 1 for i≠ j.
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