Chromatic polynomials of homeomorphism classes of graphs

We study a multilinear polynomial which subsumes the chromatic polynomials of all the graphs in a given homeomorphism class. We show that this polynomial can be extended to include further families of homeomorphic graphs, and derive some properties of its coefficients. We also prove similar results for the dual concept of graphs with multiple edges. (C) 1999 Elsevier Science B.V. All rights reserved.