  We first give an alternative proof of the Alon-Tarsi list coloring theorem.
We use the ideas from this proof to obtain the following result, which is an
additive coloring analog of the Alon-Tarsi Theorem: Let $G$ be a graph and let
$D$ be an orientation of $G$. We introduce a new digraph $\mathcal{W}(D)$, such
that if the out-degree in $D$ of each vertex $v$ is $d_v$, and if the number of
Eulerian subdigraphs of $\mathcal{W}(D)$ with an even number of edges differs
from the number of Eulerian subdigraphs of $\mathcal{W}(D)$ with an odd number
of edges, then for any assignment of lists $L(v)$ of $d_v+1$ positive integers
to the vertices of $G$, there is an additive coloring of $G$ assigning to each
vertex $v$ an element from $L(v)$. As an application, we prove an additive list
coloring result for tripartite graphs $G$ such that one of the color classes of
$G$ contains only vertices whose neighborhoods are complete.
