Decomposition formulas for the flow polynomial

The flow polynomial F G ( k ) of a graph G evaluates the number of nowhere-zero A -flows in G for any Abelian group A of order k . Suppose that C is an edge cut of G and G 1 , G 2 are the components of G − C . We give a formula expressing the flow polynomial of G from the flow polynomials of the bridgeless minors of G having edge sets equal either to C , or to E ( G 1 ) ∪ C , or to E ( G 2 ) ∪ C .