  It is proved that all 4-edge-colourings of a (sub)cubic graph are Kempe
equivalent. This resolves a conjecture of the second author. In fact, it is
found that the maximum degree Delta=3 is a threshold for Kempe equivalence of
(Delta+1)-edge-colourings, as such an equivalence does not hold in general when
Delta=4. One extra colour allows a similar result in this latter case however,
namely, when Delta<=4 it is shown that all (Delta+2)-edge-colourings are Kempe
equivalent.
