Ramsey Theory Yesterday, Today, and Tomorrow [Hardcover]

This book explores the theorys history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike.Ramsey Theory explores the history of Ramsey theory, recent developments, and promising future directions. The chapters provide historical background on the subject, and address Euclidean Ramsey theory and related coloring problems.How This Book Came into Being.- Table of Contents.- Ramsey Theory before Ramsey, Prehistory and Early History: An Essay in 13 Parts.- Eighty Years of Ramsey R(3, k). . . and Counting!.- Ramsey Numbers Involving Cycles.- On the function of ErdEs and Rogers.- Large Monochromatic Components in Edge Colorings of Graphs.- Szlams Lemma: Mutant Offspring of a Euclidean Ramsey Problem: From 1973, with Numerous Applications.- Open Problems in Euclidean Ramsey Theory.- Chromatic Number of the Plane and Its Relatives, History,Problems and Results: An Essay in 11 Parts.- Euclidean Distance Graphs on the Rational Points.- Open Problems Session.

As we learn from the preface, [Ramsey Theory: Yesterday, Today and Tomorrow] grew out of an intentionally non-traditional conference on Ramsey theory. In accordance with that, the book itself is far from being a traditional textbook or reference book on the subject&We learn far more about the history of Ramsey theory than from other sources&the promise of discussing the future is fulfilled by a very extensive list of open problems contributed by numerous participants. Sometimes it is not even clear what the best way of asking a certain question is, and we are shown the raw form of the problem, just lc-