EAN: 9783110576511

RAMSEY THEORY - XIAODONG XU MEILIAN LIANG HAIPE...

Key problems and conjectures have played an important role in promoting the development of
Ramsey theory  a field where great progress has been made during the past two decades  with
some old problems solved and many new problems proposed. The present book will be helpful to
readers who wish to learn about interesting problems in Ramsey theory  to see how they are
interconnected  and then to study them in depth. This book is the first problem book of such
scope in Ramsey theory. Many unsolved problems  conjectures and related partial results in
Ramsey theory are presented  in areas such as extremal graph theory  additive number theory 
discrete geometry  functional analysis  algorithm design  and in other areas. Most presented
problems are easy to understand  but they may be difficult to solve. They can be appreciated on
many levels and by a wide readership  ranging from undergraduate students majoring in
mathematics to research mathematicians. This collection is an essential reference for
mathematicians working in combinatorics and number theory  as well as for computer scientists
studying algorithms. Contents Some definitions and notations Ramsey theory Bi-color diagonal
classical Ramsey numbers Paley graphs and lower bounds for R(k  k) Bi-color off-diagonal
classical Ramsey numbers Multicolor classical Ramsey numbers Generalized Ramsey numbers Folkman
numbers The Erdos-Hajnal conjecture Other Ramsey-type problems in graph theory On van der
Waerden numbers and Szemeredi's theorem More problems of Ramsey type in additive number theory
Sidon-Ramsey numbers Games in Ramsey theory Local Ramsey theory Set-coloring Ramsey theory
Other problems and conjectures

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