  An acyclic coloring of a digraph as defined by Neumann-Lara is a
vertex-coloring such that no monochromatic directed cycles occur. Counting the
number of such colorings with $k$ colors can be done by counting so-called
Neumann-Lara-coflows (NL-coflows), which build a polynomial in $k$. We will
present a representation of this polynomial using totally cyclic subdigraphs,
which form a graded poset $Q$. Furthermore we will decompose our NL-coflow
polynomial, which becomes the chromatic polynomial of a digraph by
multiplication with the number of colors to the number of components, examining
the special structure of the poset of totally cyclic subdigraphs with fixed
underlying undirected graph. This decomposition will confirm the equality of
our chromatic polynomial of a digraph and the chromatic polynomial of the
underlying undirected graph in the case of symmetric digraphs.
