Book:Alan Tucker/Applied Combinatorics/Fifth Edition

Subject Matter

 * Combinatorics

Contents

 * PRELUDE


 * PART ONE: GRAPH THEORY


 * CHAPTER 1: ELEMENTS OF GRAPH THEORY
 * 1.1 Graph Models
 * 1.2 Isomorphism
 * 1.3 Edge Counting
 * 1.4 Planar Graphs
 * 1.5 Summary and References
 * Supplementary Exercises


 * CHAPTER 2: COVERING CIRCUITS AND GRAPH COLORING
 * 2.1 Euler Cycles
 * 2.2 Hamilton Circuits
 * 2.3 Graph Coloring
 * 2.4 Coloring Theorems
 * 2.5 Summary and References
 * Supplement: Graph Model for Instant Insanity
 * Supplement: Exercises


 * CHAPTER 3: TREES AND SEARCHING
 * 3.1 Properties of Trees
 * 3.2 Search Trees and Spanning Trees
 * 3.3 The Traveling Salesperson Problem
 * 3.4 Tree Analysis of Sorting Problems
 * 3.5 Summary and References


 * CHAPTER 4: NETWORK ALGORITHMS
 * 4.1 Shortest Paths
 * 4.2 Minimal Spanning Trees
 * 4.3 Network Flows
 * 4.4 Algorithmic Matching
 * 4.5 The Transportation Problem
 * 4.6 Summary and References


 * PART TWO: ENUMERATION


 * CHAPTER 5: GENERAL COUNTING METHODS FOR ARRANGEMENTS AND SELECTIONS
 * 5.1 Basic Counting Principles
 * 5.2 Simple Arrangements and Selections
 * 5.3 Arrangements and Selections with Repetitions
 * 5.4 Distributions
 * 5.5 Binomial Identities
 * 5.6 Summary and References
 * Supplement: Selected Solutions to Problems in Chapter 5


 * CHAPTER 6: GENERATING FUNCTIONS
 * 6.1 Generating Function Models
 * 6.2 Calculating Coefficients of Generating Functions
 * 6.3 Partitions
 * 6.4 Exponential Generating Functions
 * 6.5 A Summation Method
 * 6.6 Summary and References


 * CHAPTER 7: RECURRENCE RELATIONS
 * 7.1 Recurrence Relation Models
 * 7.2 Divide-and-Conquer Relations
 * 7.3 Solution of Linear Recurrence Relations
 * 7.4 Solution of Inhomogeneous Recurrence Relations
 * 7.5 Solutions with Generating Functions
 * 7.6 Summary and References


 * CHAPTER 8: INCLUSION-EXCLUSION
 * 8.1 Counting with Venn Diagrams
 * 8.2 Inclusion-Exclusion Formula
 * 8.3 Restricted Positions and Rook Polynomials
 * 8.4 Summary and Reference


 * PART THREE: ADDITIONAL TOPICS


 * CHAPTER 9: POLYA'S ENUMERATION FORMULA
 * 9.1 Equivalence and Symmetry Groups
 * 9.2 Burnside's Theorem
 * 9.3 The Cycle Index
 * 9.4 Polya's Formula
 * 9.5 Summary and References


 * CHAPTER 10: COMPUTER SCIENCE APPROACHES TO ENUMERATION
 * 10.1 Generating Permutations and Combinations and Programming Projects
 * 10.2 Formal Languages and Grammars
 * 10.3 Finite-State Machines
 * 10.4 Summary and References


 * CHAPTER 11: GAMES WITH GRAPHS
 * 11.1 Progressively Finite Games
 * 11.2 Nim-Type Games
 * 11.3 Summary and References


 * APPENDIX
 * A.1 Set Theory
 * A.2 Mathematical Induction
 * A.3 A Little Probability
 * A.4 The Pigeonhole Principle
 * A.5 Computational Complexity and NP-Completeness


 * GLOSSARY OF COUNTING AND GRAPH THEORY TERMS
 * BIBLIOGRAPHY
 * SOLUTIONS TO ODD-NUMBERED PROBLEMS
 * INDEX