The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving. As one of the most widely used book in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Although important uses of combinatorics in computer science, operations research and finite probability are mentioned, these applications are often used solely for motivation.
Part One: Graph Theory.
Chapter 1: Elements of Graph Theory.
Chapter 2: Covering Circuits and Graph coloring.
Chapter 3: Trees and Searching.
Chapter 4: Network Algorithms.
Part Two: Enumeration.
Chapter 5: General Counting Methods for Arrangements and Selections.
Chapter 6: Generating Functions.
Chapter 7: Recurrence Relations.
Chapter 8: Inclusion-Exclusion.
Part Three: Additional Topics.
Chapter 9: Polya's Enumeration Formula.
Chapter 10: Games with Grapes.
Alan Tucker is Deputy Department Chair and Undergraduate Program Director in the Department of Applied Mathematics and Statistics at SUNY Stony Brook.