Ramsey theory : unsolved problems and results /

Ramsey theory : unsolved problems and results /

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Bibliographic Details
Author / Creator:Xu, Xiaodong (Physicist), author.
Imprint:Berlin ; Boston : De Gruyter, [2018]
Description:1 online resource
Language:English
Subject:
Ramsey theory.
Combinatorial analysis.
Graph theory.
Combinatorial analysis.
Graph theory.
Ramsey theory.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/12026736
Hidden Bibliographic Details
Other authors / contributors:Liang, Meilian, author.
Luo, Haipeng, author.
ISBN:9783110576634
3110576635
9783110576702
3110576708
9783110576511
3110576511
Notes:Includes bibliographical references and index.
Online resource; title from digital title page (viewed on January 09, 2019).
Summary: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. ContentsSome definitions and notationsRamsey theoryBi-color diagonal classical Ramsey numbersPaley graphs and lower bounds for R(k, k)Bi-color off-diagonal classical Ramsey numbersMulticolor classical Ramsey numbersGeneralized Ramsey numbersFolkman numbersThe Erdò‹s-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.
Other form:Print version: Xu, Xiaodong (Physicist). Ramsey theory. Berlin ; Boston : De Gruyter, [2018] 9783110576511 3110576511
Table of Contents:
  • Some definitions and notations
  • Ramsey theory
  • Bi-color diagonal classical Ramsey numbers
  • Paley graphs and lower bounds for r(k; k)
  • Bi-color o-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
  • Epilogue.

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