On the rooted Tutte polynomial
Statistical Mechanics
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.cond-mat/9812202,
title = {On the rooted Tutte polynomial},
author = {F. Y. Wu and C. King and W. T. Lu},
journal= {arXiv preprint arXiv:cond-mat/9812202},
year = {2007}
}
Comments
plain latex, 14 pages, 2 figs., to appear in Annales de l'Institut Fourier (1999)