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Handbook of the Tutte Polynomial Monographs and Research Notes in Mathematics Series

Langue : Anglais

Coordonnateurs : Ellis-Monaghan Joanna A., Moffatt Iain

It has become a well-known fact that most graph polynomials are related to the Tutte Polynomial in some way. In fact, that area of graph polynomials has grown to such an extent that it now has its own subject classification (05C31). This handbook is the first one published on the Tutte Polynomial which is a central, heavily-studied object in the field of combinatorics with applications in a wide range of other fields such as geometry, biology and physics.

Symbols. Chapter Format. Book Concepts. Basic Identities. Standard Specializations. Foundations of the Chromatic Polynomial. Recent Advances for the Chromatic Polynomial. Why Matroids. Tutte and Chromatic Uniqueness. Connections to Other Graph Polynomials. Oriented Graphs. The Tutte Polynomial of a Matroid Perspective. Topological Extensions of the Tutte Polynomial. Connections to Knot Theory. Multivariable Generalizations. The Interlace Connection. Non-Matroidal Generalizations. The Tutte-Potts Connection. The U, W, V Polynomials. Isotropic Systems. Zeros. Codes. Computational Complexity. Computational Techniques. Algorithms. Open Questions. A Brief History. Tutte's Original Papers. Resource List.

This book is intended for mathematicians, both professionals and students working in the fields of combinatorics and discrete math. It also would be useful to physicists in the field of statistical mechanics and to computer scientists, especially those working in complexity theory.

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