On the rooted Tutte polynomial

Details On the rooted Tutte polynomial On the rooted Tutte polynomial

1998-12-11

arxiv.org/abs/cond-mat/9812202v1

Ann. Inst. Fourier (Grenoble) 49, 1103-1114 (1999).

Physics

Condensed Matter

Statistical Mechanics

plain latex, 14 pages, 2 figs., to appear in Annales de l'Institut Fourier (1999)

Scientific paper

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.

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