Graph Colouring and the Probabilistic Method

Abstract

pt. I. Preliminaries. 1. Colouring Preliminaries. 2. Probabilistic Preliminaries -- pt. II. Basic Probabilistic Tools. 3. The First Moment Method. 4. The Lovasz Local Lemma. 5. The Chernoff Bound -- pt. III. Vertex Partitions. 6. Hadwiger's Conjecture. 7. A First Glimpse of Total Colouring. 8. The Strong Chromatic Number. 9. Total Colouring Revisited -- pt. IV. A Naive Colouring Procedure. 10. Talagrand's Inequality and Colouring Sparse Graphs. 11. Azuma's Inequality and a Strengthening of Brooks' Theorem -- pt. V. An Iterative Approach. 12. Graphs with Girth at Least Five. 13. Triangle-Free Graphs. 14. The List Colouring Conjecture -- pt. VI. A Structural Decomposition. 15. The Structural Decomposition.