  In a graph $G$ of maximum degree $\Delta$ let $\gamma$ denote the largest
fraction of edges that can be $\Delta$ edge-coloured. Albertson and Haas showed
that $\gamma \geq 13/15$ when $G$ is cubic . We show here that this result can
be extended to graphs with maximum degree 3 with the exception of a graph on 5
vertices. Moreover, there are exactly two graphs with maximum degree 3 (one
being obviously the Petersen graph) for which $\gamma = 13/15$. This extends a
result given by Steffen. These results are obtained by using structural
properties of the so called $\delta$-minimum edge colourings for graphs with
maximum degree 3. Keywords : Cubic graph; Edge-colouring
