Handbook of the Tutte Polynomial and Related Topics

I. Fundamentals.

1. Graph theory.
Joanna A. Ellis-Monaghan, Iain Moffatt

2. The Tutte Polynomial for Graphs.
Joanna A. Ellis-Monaghan Iain Moffatt

3. Essential Properties of the Tutte Polynomial.
Béla Bollobás, Oliver Riordan

4. Matroid theory.
James Oxley

5. Tutte Polynomial Activities.
Spencer Backman

6. Tutte Uniqueness and Tutte Equivalence.
Joseph E. Bonin, Anna de Mier

II. Computation.

7. Computational Techniques.
Criel Merino

8. Computational Resources.
David Pearce, Gordon F. Royle

9. The Exact Complexity of the Tutte Polynomial.
Tomer Kotek, Johann A. Makowsky

10. Approximating the Tutte Polynomial.
Magnus Bordewich

III. Specializations.

11. Foundations of the Chromatic Polynomial.
Fengming Dong, Khee Meng Koh

12. Flows and Colorings.
Delia Garijo, Andrew Goodall, Jaroslav Nešeťril

13. Skein Polynomials and the Tutte Polynomial when x = y.
Joanna A. Ellis-Monaghan, Iain Moffatt

14. The Interlace Polynomial and the Tutte–Martin Polynomial.
Robert Brijder, Hendrik Jan Hoogeboom

IV. Applications.

15. Network Reliability.
Jason I. Brown, Charles J. Colbourn

16. Codes.
Thomas Britz, Peter J. Cameron

17. The Chip-Firing Game and the Sandpile Model.
Criel Merino

18. The Tutte Polynomial and Knot Theory.
Stephen Huggett

19. Quantum Field Theory Connections.
Adrian Tanasa

20. The Potts and Random-Cluster Models.
Geoffrey Grimmett

21. Where Tutte and Holant meet: a view from Counting Complexity.
Jin-Yi Cai, Tyson Williams

22. Polynomials and Graph Homomorphisms.
Delia Garijo, Andrew Goodall, Jaroslav Nešeťril, Guus Regts

V. Extensions.

23. Digraph Analogues of the Tutte Polynomial.
Timothy Y. Chow

24. Multivariable, Parameterized, and Colored Extensions of the Tutte Polynomial.
Lorenzo Traldi

25. Zeros of the Tutte Polynomial.
Bill Jackson

26. The U, V and W Polynomials.
Steven Noble

27. Valuative invariants on matroid basis polytopes Topological Extensions of the Tutte Polynomial.
Sergei Chmutov

28. The Tutte polynomial of Matroid Perspectives.
Emeric Gioan

29. Hyperplane Arrangements and the Finite Field Method.
Federico Ardila

30. Some Algebraic Structures related to the Tutte Polynomial.
Michael J. Falk, Joseph P.S. Kung

31. The Tutte Polynomial of Oriented Matroids.
Emeric Gioan

32. Valuative Invariants on Matroid Basis Polytopes.
Michael J. Falk, Joseph P.S. Kung

33. Non-matroidal Generalizations.
Gary Gordon, Elizabeth McMahon

VI History.

34. The History of Tutte–Whitney Polynomials.
Graham Farr

Biography

Joanna A. Ellis-Monaghan is a professor of discrete mathematics at the Korteweg - de Vries Instituut voor Wiskunde at the Universiteit van Amsterdam. Her research focuses on algebraic combinatorics, especially graph polynomials, as well as applications of combinatorics to DNA self-assembly, statistical mechanics, computer chip design, and bioinformatics. She also has an interest in mathematical pedagogy. She has published over 50 papers in these areas.

Iain Moffatt is a professor of mathematics in Royal Holloway, University of London. His main research interests lie in the interactions between topology and combinatorics. He is especially interested in graph polynomials, topological graph theory, matroid theory, and knot theory. He has written more than 40 papers in these areas and is also the author of the book An Introduction to Quantum and Vassiliev Knot invariants.

Ellis-Monaghan and Moffatt have authored several papers on the Tutte polynomial and related graph polynomials together as well as the book Graphs on surfaces: Dualities, Polynomials, and Knots.

"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