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Full Description
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 summarises 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.
Contents
Preface ; 1. Orbit counting and the Tutte polynomial ; 2. Eulerian and bipartite orientable matroids ; 3. Tutte-Whitney polynomials: some history and generalisations ; 4. A survey on the use of Markov chains to randomly sample colorings ; 5. Towards a matroid-minor structure theory ; 6. Random planar graphs with a fixed number of edges ; 7. Fourier analysis on finite Abelian groups: some graphical applications ; 8. Flows and ferromagnets ; 9. Approximating the Tutte polynomial ; 10. Non-separating circuits and cocircuits in matroids ; 11. Expanding the Tutte polynomial of a matroid over the independent sets ; 12. Connection matrices ; 13. Complexity of graph polynomials ; 14. Random planar graphs and the number of planar graphs ; 15. The contributions of Dominic Welsh to matroid theory ; 16. On the unknotting problem ; 17. Advances on the Erdos-Faber-Lovasz conjecture ; 18. Stochastic set-backs
