Flows in circulant graphs of odd order are sums of Hamilton cycles (Q583084)

It can be shown that, in a connected circulant graph of odd order, Hamiltonian cycles span the cycle space. In the present paper, it is shown that any flow in such a graph can be expressed as a sum of Hamiltonian cycles. This result is valid not only for flows in circulant graphs, but also for flows in any Cayley graph on any finite abelian group of odd order except for flows in the Cartesian product graph of two cycles of length 3.