Hamiltonian decompositions of Cayley graphs on Abelian groups

@article{Liu1994HamiltonianDO,
  title={Hamiltonian decompositions of Cayley graphs on Abelian groups},
  author={Jiuqiang Liu},
  journal={Discrete Mathematics},
  year={1994},
  volume={131},
  pages={163-171}
}
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= {sl,sz, s3} is a minimal generating set of A with 1 Al odd, or S={sl,s& . . . . sk} is a generating set of A such that gcd(ord(s,), ord(sj)) = 1 for i #j.