We prove that any 4-regular connected Cayley graph on a finite abelian group can be decomposed into two hamiltonian cycles. This answers a partial case of Alspach's conjecture concerning hamiltonian decompositions of 2k-regular connected Cayley graphs. As a corollary we obtain the hamiltonian decomposition of 2-jump circulant graphs, also called double loops. © 1989.
Bermond, J. C., Favaron, O., & Maheo, M. (1989). Hamiltonian decomposition of Cayley graphs of degree 4. Journal of Combinatorial Theory, Series B, 46(2), 142–153. https://doi.org/10.1016/0095-8956(89)90040-3