  Chromatic polynomials have been studied extensively, giving us results such
as the Fundamental Reduction Theorem and closed formulas for the chromatic
polynomials of common classes of graphs. Though, none of those extend to the
context of fractional colorings. We thus present closed formulas for the
"fractional" chromatic polynomial - a function that counts the number of
distinct $b$-fold $\lambda$-colorings on a given graph - of complete graphs,
trees and forests, as well as a generalized form of the Fundamental Reduction
Theorem.
