Contents PREFACE xi ACKNOWLEDGMENTS PARTI METHODS 1 The Basic Method 1.1 The Probabilistic Method,3 Graph Theory.5 Combinatorics,9 1.4 Combinatorial Number Theory,11 1.5 Disjoint Pairs,12 1.6 Independent Sets and List Coloring.13 1.7 Exercises,16 The Erdos-Ko-Rado Theorem,18 2 Linearity of Expectation 19 oContents PREFACE xiii ACKNOWLEDGMENTS xv PART I METHODS 1 1 The Basic Method 3 1.1 The Probabilistic Method, 3 1.2 Graph Theory, 5 1.3 Combinatorics, 9 1.4 Combinatorial Number Theory, 11 1.5 Disjoint Pairs, 12 1.6 Independent Sets and List Coloring, 13 1.7 Exercises, 16 The Erd ˝os–Ko–Rado Theorem, 18 2 Linearity of Expectation 19 2.1 Basics, 19 2.2 Splitting Graphs, 20 2.3 Two Quickies, 22 2.4 Balancing Vectors, 23