The flow polynomial \pol{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 $G$ has an edge cut $C$ that divides $G$ into two
subgraphs $G_1$ and $G_2$ (having the same components as $G-C$) such
that each edge of $C$ has exactly one end in one of them. We give a
formula expressing the flow polynomial of $G$ from the flow
polynomials of the bridgeless graphs arising from $G$ after deleting
or contracting all edges either from $G_1$, or from $G_2$, or from
$G_1\cup G_2$.
