A mixed graph is a graph with directed edges, called arcs, and undirected edges. A k-coloring of the vertices is proper if colors from 1,2,...,k are assigned to each vertex such that u and v have different colors if uv
Nearby in the stack
is an edge, and the color of
u
is less than or equal to (resp. strictly less than) the color of
v
if
uv
is an arc. The weak (resp. strong) chromatic polynomial of a mixed graph counts the number of proper
k
-colorings. Using order polynomials of partially ordered sets, we establish a reciprocity theorem for weak chromatic polynomials giving interpretations of evaluations at negative integers.