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Combinatorics, Complexity, and Chance


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Table of Contents

Preface 1: Peter Cameron: Orbit counting and the Tutte polynomial 2: Laura Chavez Lomeli and L.A. Goddyn: Eulerian and bipartite orientable matroids 3: Graham Farr: Tutte-Whitney polynomials: some history and generalisations 4: Alan Frieze and Eric Vigoda: A survey on the use of Markov chains to randomly sample colorings 5: Jim Geelen, Bert Gerards, Geoff Whittle: Towards a matroid-minor structure theory 6: Stefanie Gerke, Colin McDiarmid, Angelika Steger, Andreas Weissl: Random planar graphs with a fixed number of edges 7: Andrew Goodall: Fourier analysis on finite Abelian groups: some graphical applications 8: Geoffrey Grimmett: Flows and ferromagnets 9: Mark Jerrum: Approximating the Tutte polynomial 10: Braulio Maia Junior, Manoel Lemos, T.R.B. Melo: Non-separating circuits and cocircuits in matroids 11: Koko Kalambay Kayibi: Expanding the Tutte polynomial of a matroid over the independent sets 12: Laszlo Lovasz: Connection matrices 13: Steven Noble: Complexity of graph polynomials 14: Marc Noy: Random planar graphs and the number of planar graphs 15: James Oxley: The contributions of Dominic Welsh to matroid theory 16: J.L. Ramirez Alfonsin: On the unknotting problem 17: David Romero, Abdon Sanchez-Arroyo: Advances on the Erdoes-Faber-Lovasz conjecture 18: David Stirzaker: Stochastic set-backs

About the Author

Dominic Welsh has been the resident mathematician at Merton College, Oxford, for about 40 years, where he has guided and influenced generations of undergraduate and graduate students. Prior to his formal retirement in 2005, he was a Professor in the Mathematical Institute at Oxford University, where he served as Chairman for five years. Dominic Welsh is a leading figure worldwide in aspects of combinatorics and probability, including matroids, complexity, and percolation. Geoffrey Grimmett graduated under Dominic Welsh in 1971. He worked in Bristol University for 16 years before moving to Cambridge in 1992 as Professor of Mathematical Statistics. He is currently Head of the Department of Pure Mathematics and Mathematical Statistics, and a professorial fellow of Churchill College. His main interests lie in probability theory and rigorous statistical mechanics, and he is the author of successful texts on percolation theory and the random-cluster model. Colin McDiarmid gained his DPhil under Dominic Welsh in 1975. After a brief spell at the London School of Economics he became a fellow of Wolfson College, Oxford and then a fellow of Corpus Christi College. He is currently Professor of Combinatorics and Head of the Department of Statistics. His main interests lie in combinatorial theory, particularly in random structures and algorithms.


Dominic Welsh has made major contributions to the fields of combinatorics and discrete probability. This volume summarises and reviews the consistent themes from his work through a series of articles written by renowed experts. These articles contain original research work, set in a broader context by the inclusion of review material. * L'enseignement Mathematique *

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