CONTENTS 6.4 Linear Extensions of Partially Ordered Sets,97 6.5 Exercises,99 Turan's Theorem,100 7 Martingales and Tight Concentration 103 7.1 Definitions,103 7.2 Large Deviations,105 7.3 Chromatic Number,107 7.4 Two General Settings,109 75 Four Illustrations,113 7.6 Talagrand's Inequality,116 7.7 Applications of Talas Kim-VuPo Exercises,123 Weierstrass Approximation Theorem,124 8 The Poisson Paradigm 127 8.1 The Janson Inequalities,127 8.2 The Proofs,129 8.3 Brun's Sieve 132 84 Large Deviations,135 只5 Counting Extensions,137 86 Counting 87 Further 142 8.8 Exercises,143 Local Coloring,144 147 9.1 The Quadratic Residue Tournaments,148 9.2 Eigenvalues and Expanders,151 9.3 Quasirandom Graphs,157 94 Szemeredi's Regularity Lemma.165 9.5 Graphons,170 9.6 Exercises,172 Random Walks,174 PARTⅡTOPICS 177 10 Random Graphs 179 10.1 Subgraphs,180CONTENTS ix 6.4 Linear Extensions of Partially Ordered Sets, 97 6.5 Exercises, 99 Turán’s Theorem, 100 7 Martingales and Tight Concentration 103 7.1 Definitions, 103 7.2 Large Deviations, 105 7.3 Chromatic Number, 107 7.4 Two General Settings, 109 7.5 Four Illustrations, 113 7.6 Talagrand’s Inequality, 116 7.7 Applications of Talagrand’s Inequality, 119 7.8 Kim–Vu Polynomial Concentration, 121 7.9 Exercises, 123 Weierstrass Approximation Theorem, 124 8 The Poisson Paradigm 127 8.1 The Janson Inequalities, 127 8.2 The Proofs, 129 8.3 Brun’s Sieve, 132 8.4 Large Deviations, 135 8.5 Counting Extensions, 137 8.6 Counting Representations, 139 8.7 Further Inequalities, 142 8.8 Exercises, 143 Local Coloring, 144 9 Quasirandomness 147 9.1 The Quadratic Residue Tournaments, 148 9.2 Eigenvalues and Expanders, 151 9.3 Quasirandom Graphs, 157 9.4 Szemerédi’s Regularity Lemma, 165 9.5 Graphons, 170 9.6 Exercises, 172 Random Walks, 174 PART II TOPICS 177 10 Random Graphs 179 10.1 Subgraphs, 180