Graph polynomials and their applications I: The Tutte polynomial

Details Graph polynomials and their applications I: The Tutte polynomial Graph polynomials and their applications I: The Tutte polynomial

2008-03-20

arxiv.org/abs/0803.3079v2

Mathematics

Combinatorics

This is a preliminary version of one of two book chapters for inclusion in a volume on graph structures. Minor changes

Scientific paper

In this survey of graph polynomials, we emphasize the Tutte polynomial and a selection of closely related graph polynomials. We explore some of the Tutte polynomial's many properties and applications and we use the Tutte polynomial to showcase a variety of principles and techniques for graph polynomials in general. These include several ways in which a graph polynomial may be defined and methods for extracting combinatorial information and algebraic properties from a graph polynomial. We also use the Tutte polynomial to demonstrate how graph polynomials may be both specialized and generalized, and how they can encode information relevant to physical applications. We conclude with a brief discussion of computational complexity considerations.

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