A note on Hamiltonian decompositions of Cayley graphs (Q1912810)

Alspach posed the following problem: Does every \(2k\)-regular Cayley graph \((k> 1)\) on an abelian group admit Hamilton decomposition? Bermond et al. proved that every 4-regular Cayley graph \(\text{Cay}(S, G)\) on a finite abelian group \(G\) is decomposable into two Hamilton cycles, if a generating set \(S\) does not contain elements of order two. The authors remove this restriction and get the theorem: Every 4-regular Cayley graph \(\text{Cay}(S, G)\) is decomposable into two Hamilton cycles.