Updated with new material, this Fifth Edition of the most widely used book in combinatorial problems explains how to reason and model combinatorically. It also stresses the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Combinatorical reasoning underlies all analysis of computer systems. It plays a similar role in discrete operations research problems and in finite probability. This book seeks to develop proficiency in basic discrete math problem solving in the way that a calculus text develops proficiency in basic analysis problem solving.Prelude.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. Computer Science Approaches to Enumeration.Chapter 11. Games with Graphs.Appendix.Glossary of Counting.Graph Theory Terms.Bibliography.Solutions to Odd-Numbered Problems.Index….a well-structured text that addresses a broad range of topics… It is well presented, written clearly and easy to follow. (Times Higher Education Supplement, November 2007)Alan Tucker is Deputy Department Chair and Undergraduate Program Director in the Department of Applied Mathematics and Statistics at SUNY Stony Brook.