Combinatorics, Complexity, and Chance A

Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation, and has taught, influenced and inspired generations of students and researchers in mathematics. This volume summarizes and reviews the consistent themes from his work through a series of articles written by renowned experts. These articles contain original research work, set in a broader context by the inclusion of review material. As a reference text in its own right, this book will be valuable to academic researchers, research students, and others seeking an introduction to the relevant contemporary aspects of these fields.

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.

List of contributors	p. ix
Orbit counting and the Tutte polynomial	p. 1
Eulerian and bipartite orientable matroids	p. 11
Tutte-Whitney polynomials: some history and generalizations	p. 28
A survey on the use of Markov chains to randomly sample colourings	p. 53
Towards a matroid-minor structure theory	p. 72
Random planar graphs with given average degree	p. 83
Fourier analysis on finite abelian groups: some graphical applications	p. 103
Flows and ferromagnets	p. 130
Approximating the Tutte polynomial	p. 144
Non-separating circuits and cocircuits in matroids	p. 162
Expanding the Tutte polynomial of a matroid over the independent sets	p. 172
Connection matrices	p. 179
Complexity of graph polynomials	p. 191
Random planar graphs and the number of planar graphs	p. 213
The contributions of Dominic Welsh to matroid theory	p. 234
On the unknotting problem	p. 260
Advances on the Erdös-Faber-Lovasz conjecture	p. 272
Stochastic set-backs	p. 285
Index	p. 299
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Combinatorics, Complexity, and Chance A Tribute to Dominic Welsh

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