Ramsey Theory

Ramsey Theory has become the reference book its field as it contains most of the results and techniques in classical Ramsey Theory and remains the only book to cover the broad spectrum of the subject area. It provides both full proofs (in many cases more than one proof to give different vantage points) and a leisurely discussion of the major theorems, such as Ramsey's Theorem, van der Waerden's Theorem, the Hales-Jewett Theorem, and Rado's Theorem.

A new chapter on Graph Ramsey has been added in light of recent emphasis on the topic within the mathematics community, and numerous new exercises have been added to help make the book more classroom friendly.

This book also includes a complete treatment of Saharon Shelah's proof, which avoids double induction, involves fast growing functions, and is elementary in nature. A historical perspective is included and discusses the fundamental papers of Ramsey in 1930, and of Erdos and Szekeres in 1935.

About the authors RONALD L. GRAHAM is Adjunct Director for Research at AT&T Bell Laboratories, and University Professor of the Mathematical Sciences at Rutgers University. He is coauthor of Concrete Mathematics and of Old and New Problems in Combinatorial Number Theory, and serves on the editorial boards of more than 25 technical journals. He received his PhD in mathematics from the University of California, Berkeley. BRUCE L. ROTHSCHILD is Professor of Mathematics at the University of California, Los Angeles. He is Managing Editor of the Journal of Combinatorial Theory. He received his PhD in mathematics from Yale University. JOEL H. SPENCER is a professor of mathematics and computer science at the Courant Institute. He is the author of Ten Lectures on the Probabilistic Method and the editor of Random Structures and Algorithms. He received his PhD in mathematics from Harvard University.