  The Tutte polynomial is a generalization of the chromatic polynomial of graph
colorings. Here we present an extension called the rooted Tutte polynomial,
which is defined on a graph where one or more vertices are colored with
prescribed colors. We establish a number of results pertaining to the rooted
Tutte polynomial, including a duality relation in the case that all roots
reside around a single face of a planar graph. The connection with the Potts
model is also reviewed.
