### Proof of Theorem 17.2

Leonardo Carlos da Cruz has pointed out an error in the proof of Theorem 17.2.

The sentence:

Because the degree of $u$ in $G\setminus e$ is at most $\Delta – 1$, at least one colour $i$ is available at $u$, hence represented at $v$. Likewise, at least one colour $j$ is available at $v$ and represented at $u$.

should read: