Journal of Statistical Physics, VoL 52, No. 1/2, 1988. p. 99-112.
Elementary exposition is given of some recent developments in studies of graph-theoretic aspects of the Potts model. Topics discussed include graphical expansions of the Potts partition function and correlation functions and their relationships with the chromatic, dichromatic, and flow polynomials occurring in graph theory. It is also shown that the Potts model realization of these classic graph-theoretic problems provides alternate and direct proofs of properties established heretofore only in the context of formal graph theory.