Handbook of the Tutte Polynomial and Related Topics

The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied graph polynomials.

Handbook of the Tutte Polynomial and Related Topics is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters written by experts in the field, which collectively offer a concise overview of the polynomial?s many properties and applications. Each chapter covers a different aspect of the Tutte polynomial and contains the central results and references for its topic. The chapters are organized into six parts. Part I describes the fundamental properties of the Tutte polynomial, providing an overview of the Tutte polynomial and the necessary background for the rest of the handbook. Part II is concerned with questions of computation, complexity, and approximation for the Tutte polynomial; Part III covers a selection of related graph polynomials; Part IV discusses a range of applications of the Tutte polynomial to mathematics, physics, and biology; Part V includes various extensions and generalizations of the Tutte polynomial; and Part VI provides a history of the development of the Tutte polynomial.

• Written in an accessible style for non-experts, yet extensive enough for experts








• Serves as a comprehensive and accessible introduction to the theory of graph polynomials for researchers in mathematics, physics, and computer science








• Provides an extensive reference volume for the evaluations, theorems, and properties of the Tutte polynomial and related graph, matroid, and knot invariants








• Offers broad coverage, touching on the wide range of applications of the Tutte polynomial and its various specializations

"This is a comprehensive reference text on the Tutte polynomial, including its applications and extensions. The book consists of 34 relatively short chapters written by different contributing authors. The individual contributors present the most important theorems in their respective fields and illustrate them with examples. Each chapter ends with a list of open problems. Two brief introductory chapters by the editors?Ellis-Monaghan (Univ. of Amsterdam) and Moffatt (Royal Holloway, University of London)?cover the basic definitions and computational results for Tutte polynomials. The next two-thirds of the book are devoted to applications and extensions, that is, uses and occurrences of Tutte polynomials outside graph theory or matroid theory. Hyperplane arrangements, quantum field theory, network reliability, the sandpile model, and chipfiring games are a few examples of the topics treated. The book concludes with a chapter on the history of the subject written by Graham Farr. It follows from the nature of the volume (i.e., no proofs, no exercises, very broad topical coverage, and more than 50 authors) that classroom use of the book is unlikely. Nonetheless, this work is likely to become the most frequently consulted reference on Tutte polynomials."

Summing Up: Highly recommended. Graduate students and faculty.

-Choice Review