Ramsey Theory: Unsolved Problems and Results
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 lear...
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
[2018]
|
| Schlagworte: | |
| Online-Zugang: | DE-1043 DE-1046 DE-858 DE-898 DE-859 DE-860 DE-91 DE-706 DE-739 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | 1 online resource (190 p.) |
| ISBN: | 9783110576702 |
| DOI: | 10.1515/9783110576702 |
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| 505 | 8 | |a Frontmatter -- - Preface - Xu, Xiaodong -- - Contents -- - 1. Some Definitions And Notations -- - 2. Ramsey Theory -- - 3. Bi-Color Diagonal Classical Ramsey Numbers -- - 4. Paley Graphs And Lower Bounds For R(K, K) -- - 5. Bi-Color Off-Diagonal Classical Ramsey Numbers -- - 6. Multicolor Classical Ramsey Numbers -- - 7. Generalized Ramsey Numbers -- - 8. Folkman Numbers -- - 9. The Erdős–Hajnal Conjecture -- - 10. Other Ramsey-Type Problems In Graph Theory -- - 11. On Van Der Waerden Numbers And Szemerédi’S Theorem -- - 12. More Problems Of Ramsey Type In Additive Number Theory -- - 13. Sidon–Ramsey Numbers -- - 14. Games In Ramsey Theory -- - 15. Local Ramsey Theory -- - 16. Set-Coloring Ramsey Theory -- - 17. Other Problems And Conjectures -- - Epilogue -- - Bibliography -- - Index. - Mode of access: Internet via World Wide Web | |
| 520 | |a 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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Datensatz im Suchindex
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| contents | Frontmatter -- - Preface - Xu, Xiaodong -- - Contents -- - 1. Some Definitions And Notations -- - 2. Ramsey Theory -- - 3. Bi-Color Diagonal Classical Ramsey Numbers -- - 4. Paley Graphs And Lower Bounds For R(K, K) -- - 5. Bi-Color Off-Diagonal Classical Ramsey Numbers -- - 6. Multicolor Classical Ramsey Numbers -- - 7. Generalized Ramsey Numbers -- - 8. Folkman Numbers -- - 9. The Erdős–Hajnal Conjecture -- - 10. Other Ramsey-Type Problems In Graph Theory -- - 11. On Van Der Waerden Numbers And Szemerédi’S Theorem -- - 12. More Problems Of Ramsey Type In Additive Number Theory -- - 13. Sidon–Ramsey Numbers -- - 14. Games In Ramsey Theory -- - 15. Local Ramsey Theory -- - 16. Set-Coloring Ramsey Theory -- - 17. Other Problems And Conjectures -- - Epilogue -- - Bibliography -- - Index. - Mode of access: Internet via World Wide Web |
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| dewey-full | 511/.66 |
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| discipline | Mathematik |
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| spelling | Xu, Xiaodong Verfasser (DE-588)116438466X aut Ramsey Theory Unsolved Problems and Results Xiaodong Xu, Meilian Liang, Haipeng Luo. In Gemeinschaft mit: University of Science & Technology Berlin De Gruyter [2018] 1 online resource (190 p.) txt rdacontent c rdamedia cr rdacarrier Frontmatter -- - Preface - Xu, Xiaodong -- - Contents -- - 1. Some Definitions And Notations -- - 2. Ramsey Theory -- - 3. Bi-Color Diagonal Classical Ramsey Numbers -- - 4. Paley Graphs And Lower Bounds For R(K, K) -- - 5. Bi-Color Off-Diagonal Classical Ramsey Numbers -- - 6. Multicolor Classical Ramsey Numbers -- - 7. Generalized Ramsey Numbers -- - 8. Folkman Numbers -- - 9. The Erdős–Hajnal Conjecture -- - 10. Other Ramsey-Type Problems In Graph Theory -- - 11. On Van Der Waerden Numbers And Szemerédi’S Theorem -- - 12. More Problems Of Ramsey Type In Additive Number Theory -- - 13. Sidon–Ramsey Numbers -- - 14. Games In Ramsey Theory -- - 15. Local Ramsey Theory -- - 16. Set-Coloring Ramsey Theory -- - 17. Other Problems And Conjectures -- - Epilogue -- - Bibliography -- - Index. - Mode of access: Internet via World Wide Web 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 In English Combinatorial analysis Graph theory Ramsey theory Liang, Meilian Verfasser (DE-588)1164384953 aut Luo, Haipeng Verfasser (DE-588)1164384767 aut Erscheint auch als Druck-Ausgabe 978-3-11-057651-1 https://doi.org/10.1515/9783110576702 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Xu, Xiaodong Liang, Meilian Luo, Haipeng Ramsey Theory Unsolved Problems and Results Frontmatter -- - Preface - Xu, Xiaodong -- - Contents -- - 1. Some Definitions And Notations -- - 2. Ramsey Theory -- - 3. Bi-Color Diagonal Classical Ramsey Numbers -- - 4. Paley Graphs And Lower Bounds For R(K, K) -- - 5. Bi-Color Off-Diagonal Classical Ramsey Numbers -- - 6. Multicolor Classical Ramsey Numbers -- - 7. Generalized Ramsey Numbers -- - 8. Folkman Numbers -- - 9. The Erdős–Hajnal Conjecture -- - 10. Other Ramsey-Type Problems In Graph Theory -- - 11. On Van Der Waerden Numbers And Szemerédi’S Theorem -- - 12. More Problems Of Ramsey Type In Additive Number Theory -- - 13. Sidon–Ramsey Numbers -- - 14. Games In Ramsey Theory -- - 15. Local Ramsey Theory -- - 16. Set-Coloring Ramsey Theory -- - 17. Other Problems And Conjectures -- - Epilogue -- - Bibliography -- - Index. - Mode of access: Internet via World Wide Web Combinatorial analysis Graph theory Ramsey theory |
| title | Ramsey Theory Unsolved Problems and Results |
| title_auth | Ramsey Theory Unsolved Problems and Results |
| title_exact_search | Ramsey Theory Unsolved Problems and Results |
| title_full | Ramsey Theory Unsolved Problems and Results Xiaodong Xu, Meilian Liang, Haipeng Luo. In Gemeinschaft mit: University of Science & Technology |
| title_fullStr | Ramsey Theory Unsolved Problems and Results Xiaodong Xu, Meilian Liang, Haipeng Luo. In Gemeinschaft mit: University of Science & Technology |
| title_full_unstemmed | Ramsey Theory Unsolved Problems and Results Xiaodong Xu, Meilian Liang, Haipeng Luo. In Gemeinschaft mit: University of Science & Technology |
| title_short | Ramsey Theory |
| title_sort | ramsey theory unsolved problems and results |
| title_sub | Unsolved Problems and Results |
| topic | Combinatorial analysis Graph theory Ramsey theory |
| topic_facet | Combinatorial analysis Graph theory Ramsey theory |
| url | https://doi.org/10.1515/9783110576702 |
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