Complexity: Knots, Colourings and Countings

These notes are based on a series of lectures given at the Advanced Research Institute of Discrete Applied Mathematics, Rutgers University.

Dominic Welsh (Author)

9780521457408, Cambridge University Press

Paperback, published 12 August 1993

172 pages, 70 line figures
22.7 x 15.1 x 1.2 cm, 0.259 kg

"A clear and up-to-date survey of what's known--and what's still unknown." American Mathematical Monthly

These notes are based on a series of lectures given at the Advanced Research Institute of Discrete Applied Mathematics held at Rutgers University. Their aim is to link together algorithmic problems arising in knot theory, statistical physics and classical combinatorics. Apart from the theory of computational complexity concerned with enumeration problems, introductions are given to several of the topics treated, such as combinatorial knot theory, randomised approximation algorithms, percolation and random cluster models. To researchers in discrete mathematics, computer science and statistical physics, this book will be of great interest, but any non-expert should find it an appealing guide to a very active area of research.

1. The complexity of enumeration
2. Knots and links
3. Colourings, flows and polynomials
4. Statistical physics
5. Link polynomials
6. Complexity questions
7. The complexity of uniqueness and parity
8. Approximation and randomisation
References.

Subject Areas: Probability & statistics [PBT]