Graph Colouring and the Probabilistic Method

Table of Contents

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   Book Overview
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   Chapter 1 Colouring Preliminaries
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   Chapter 2 Probabilistic Preliminaries
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   Chapter 3 The First Moment Method
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   Chapter 4 The Lovász Local Lemma
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   Chapter 5 The Chernoff Bound
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   Chapter 6 Hadwiger’s Conjecture
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   Chapter 7 A First Glimpse of Total Colouring
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   Chapter 8 The Strong Chromatic Number
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    Chapter 9 Total Colouring Revisited
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    Chapter 10 Talagrand’s Inequality and Colouring Sparse Graphs
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    Chapter 11 Azuma’s Inequality and a Strengthening of Brooks’ Theorem
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    Chapter 12 Graphs with Girth at Least Five
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    Chapter 13 Triangle-Free Graphs
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    Chapter 14 The List Colouring Conjecture
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    Chapter 15 The Structural Decomposition
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    Chapter 16 ω, Δ and χ
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    Chapter 17 Near Optimal Total Colouring I: Sparse Graphs
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    Chapter 18 Near Optimal Total Colouring II: General Graphs
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    Chapter 19 Generalizations of the Local Lemma
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    Chapter 20 A Closer Look at Talagrand’s Inequality
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    Chapter 21 Finding Fractional Colourings and Large Stable Sets
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    Chapter 22 Hard-Core Distributions on Matchings
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    Chapter 23 The Asymptotics of Edge Colouring Multigraphs
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    Chapter 24 The Method of Conditional Expectations
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    Chapter 25 Algorithmic Aspects of the Local Lemma