(Each Chapter concludes with "Historical Notes," "Supplementary Exercises," "Computer Projects," and "Suggested Readings.").1: An Introduction to Combinatorial Problems and Techniques Section 1.1 The Time to Complete a ProjectSection 1.2 A Matching ProblemSection 1.3 A Knapsack ProblemSection 1.4 Algorithms and Their EfficiencyHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 2: Sets, Relations, and Functions Section 2.1 Set OperationsSection 2.2 Equivalence RelationsSection 2.3_ Partial Ordering RelationsSection 2.4 FunctionsSection 2.5 Mathematical InductionSection 2.6 ApplicationsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 3: Coding Theory Section 3.1 CongruenceSection 3.2 The Euclidean Algorithm and Diophantine EquationsSection 3.3 The RSA MethodSection 3.4 Error-Detecting and Error-Correcting CodesSection 3.5 Matrix CodesSection 3.6 Matrix Codes That Correct All Single-Digit ErrorsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 4: Graphs Section 4.1 Graphs and Their RepresentationsSection 4.2 Paths and CircuitsSection 4.3 Shortest Paths and DistanceSection 4.4 Coloring a GraphSection 4.5 Directed Graphs and MultigraphsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 5: Trees Section 5.1 Properties of TreesSection 5.2 Spanning TreesSection 5.3 Depth-First SearchSection 5.4 Rooted TreesSection 5.5 Binary Trees and TraversalsSection 5.6 Optimal Binary Trees and Binary Search TreesHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 6: Matching Section 6.1 Systems of Distinct RepresentativesSection 6.2 Matchings in GraphsSection 6.3 A Matching AlgorithmSection 6.4 Applications of the AlgorithmSection 6.5 The Hungarian MethodHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 7: Network Flows Section 7.1 Flows and CutsSection 7.2 A Flow Augmentation AlgorithmSection 7.3 The Max-Flow Min-Cut TheoremSection 7.4 Flows and MatchingsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 8: Counting Techniques Section 8.1 Pascal's Triangle and the Binomial TheoremSection 8.3 Permutations and CombinationsSection 8.4 Arrangements and Selections with RepetitionsSection 8.5 ProbabilitySection 8.6* The Principle of Inclusion-ExclusionSection 8.7* Generating Permutations and r -CombinationsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 9: Recurrence Relations and Generating Functions Section 9.1 Recurrence RelationsSection 9.2 The Method of IterationSection 9.3 Linear Difference Equations with Constant CoefficientsSection 9.4* Analyzing the Efficiency of Algorithms with Recurrence RelationsSection 9.5 Counting with Generating FunctionsSection 9.6 The Algebra of Generating FunctionsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 10: Combinatorial Circuits and Finite State Machines Section 10.1 Logical GatesSection 10.2 Creating Combinatorial CircuitsSection 10.3 Karnaugh MapsSection 10.4 Finite State MachinesHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings Appendix A: An Introduction to Logic and Proof Section A.1 Statements and ConnectivesSection A.2 Logical EquivalenceSection A.3 Methods of ProofHistorical NotesSupplementary ExercisesSuggested Readings Appendix B Matrices Historical Notes Appendix C The Algorithms in This Book Bibliography Answers to odd-numbered exercises Index