In the first video of Week 10, we apply Azuma's inequality to concentrate the chromatic number of the random graph G(n,p); in particular to just 4 values if p is large enough.
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Probabilistic Methods 13-1: Large Independent Sets in Triangle Free Graphs
Probabilistic Methods 12-2: Dependent Random Choice
Probabilistic Methods 12-1: Crossing Lemma
Probabilistic Methods 11-2: Brun's Sieve and the Poisson Paradigm
Probabilistic Methods 11-1: Janson's Inequality
Probabilistic Methods 10-2: Applying Concentration Inequalities, Part 2
Probabilistic Methods 10-1: Applying Concentration Inequalities, Part 1
Probabilistic Methods 9-1: Talagrand's Inequality
Probabilistic Methods 8-2: Concentration Inequalities
Probabilistic Methods 8-1: FKG Inequality
Probabilistic Methods 7-2: Four Functions Theorem
Probabilistic Methods 7-1: Moser-Tardos Algorithm
Probabilistic Methods 6-2: Applying the Local Lemma
Probabilistic Methods 6-1: Local Lemma
Probabilistic Methods 5-2: Proving Pippenger-Spencer
Probabilistic Methods: 5-1 Rodl's Nibble
Graph Theory 1-4: Coloring and Brooks' Theorem.
Graph Theory 1-2: Writing Guidelines
Graph Theory 3-2: Proof of Vizing's Theorem
Graph Theory 3-1: Edge Coloring
Graph Theory 3-3: List Edge Coloring
Graph Theory 2-1: An Informal Proof of Brooks Theorem
Graph Theory 1-3: A Writing Example
Graph Theory 2-2: Towards a Formal Proof of Brooks' Theorem