The 3-flow conjecture of Tutte is that every bridgeless graph
without a 3-edge cut has a nowhere-zero 3-flow. We present two
equivalent versions of this conjecture. The first one is that it
suffices to prove the 3-flow conjecture for 5-edge-connected graphs.
The second variant is that every 4-edge-connected graph has a
nowhere-zero $\Bbb Z_3$-flow with prescribed values on edges
incident to a vertex of valency 4 or 5.
