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Ramsey Theory : Unsolved Problems and Results

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Title: Ramsey Theory : Unsolved Problems and Results
Description: 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 Erdős–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
Authors: Xiaodong Xu, Meilian Liang, Haipeng Luo
Resource Type: eBook.
Subjects: Graph theory, Ramsey theory, Combinatorial analysis
Categories: MATHEMATICS / Algebra / General, MATHEMATICS / Number Theory, MATHEMATICS / Combinatorics
Database: eBook Collection (EBSCOhost)
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An: 1868110
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  Data: Ramsey Theory : Unsolved Problems and Results
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  Label: Description
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  Data: 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 Erdős–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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  Data: <searchLink fieldCode="AR" term="%22Xiaodong+Xu%22">Xiaodong Xu</searchLink><br /><searchLink fieldCode="AR" term="%22Meilian+Liang%22">Meilian Liang</searchLink><br /><searchLink fieldCode="AR" term="%22Haipeng+Luo%22">Haipeng Luo</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Ramsey+theory%22">Ramsey theory</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+analysis%22">Combinatorial analysis</searchLink>
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    Classifications:
      – Code: 511.66
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Graph theory
        Type: general
      – SubjectFull: Ramsey theory
        Type: general
      – SubjectFull: Combinatorial analysis
        Type: general
    Titles:
      – TitleFull: Ramsey Theory : Unsolved Problems and Results
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Xiaodong Xu
      – PersonEntity:
          Name:
            NameFull: Meilian Liang
      – PersonEntity:
          Name:
            NameFull: Haipeng Luo
      – PersonEntity:
          Name:
            NameFull: Xiaodong Xu
      – PersonEntity:
          Name:
            NameFull: Meilian Liang
      – PersonEntity:
          Name:
            NameFull: Haipeng Luo
    IsPartOfRelationships:
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2018
            – D: 05
              M: 09
              Type: profile
              Y: 2018
          Identifiers:
            – Type: isbn-print
              Value: 9783110576511
            – Type: isbn-electronic
              Value: 9783110576634
            – Type: isbn-electronic
              Value: 9783110576702
          Titles:
            – TitleFull: Ramsey Theory : Unsolved Problems and Results
              Type: main
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