  The \emph{total graph} $T(G)$ of a multigraph $G$ has as its vertices the set
of edges and vertices of $G$ and has an edge between two vertices if their
corresponding elements are either adjacent or incident in $G$. We show that if
$G$ has maximum degree $\Delta(G)$, then $T(G)$ is $(2\Delta(G)-1)$-choosable.
We give a linear-time algorithm that produces such a coloring. The best
previous general upper bound for $\Delta(G) > 3$ was
$\floor{\frac32\Delta(G)+2}$, by Borodin et al. When $\Delta(G)=4$, our
algorithm gives a better upper bound. When $\Delta(G)\in\{3,5,6\}$, our
algorithm matches the best known bound. However, because our algorithm is
significantly simpler, it runs in linear time (unlike the algorithm of Borodin
et al.).
