  The chromatic polynomial and its generalization, the chromatic symmetric
function, are two important graph invariants. Celebrated theorems of Birkhoff,
Whitney, and Stanley show how both objects can be expressed in three different
ways: as sums over all spanning subgraphs, as sums over spanning subgraphs with
no broken circuits, and in terms of acyclic orientations with compatible
colorings. We establish all six of these expressions bijectively. In fact, we
do this with only two bijections, as the proofs in the symmetric function
setting are obtained using the same bijections as in the polynomial case and
the bijection for broken circuits is just a restriction of the one for all
spanning subgraphs.
