| Description |
1 online resource (xxx, 607 pages) : illustrations |
| Contents |
pt. 1. Merry-go-round -- pt. 2. Colored plane -- pt. 3. Coloring graphs -- pt. 4. Coloring maps -- pt. 5. Colored graphs -- pt. 6. The Ramsey principle -- pt. 7. Colored integers : Ramsey theory before Ramsey and its aftermath -- pt. 8. Colored polygons : Euclidean Ramsey theory -- pt. 9. Colored integers in service of chromatic number of the plane -- pt. 10. Predicting the future -- pt. 11. Farewell to the reader |
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A story of colored polygons and arithmetic progressions -- Chromatic number of the plane : the problem -- Chromatic number of the plane : an historical essay -- Polychromatic number of the plane and results near the lower bound -- De Bruijn-Erdős reduction to finite sets and results near the lower bound -- Polychromatic number of the plane and results near the upper bound -- Continuum of 6-colorings of the plane -- Chromatic number of the plane in special circumstances -- Measurable chromatic number of the plane -- Coloring in space -- Rational coloring -- Chromatic number of a graph -- Dimension of a graph -- Embedding 4-chromatic graphs in the plane -- Embedding world records -- Edge chromatic number of a graph -- Carsten Thomassen's 7-color theorem -- How the four-color conjecture was born -- Victorian comedy of errors and colorful progress -- Kempe-Heawood's five-color theorem and Tait's equivalence -- The four-color theorem -- The great debate -- How does one color infinite maps? A bagatelle -- Chromatic number of the plane meets map coloring : Townsend-Woodall's 5-color theorem -- Paul Erdős -- De Bruijn-Erdős's theorem and its history -- Edge colored graphs : Ramsey and Folkman numbers -- From pigeonhole principle to Ramsey principle -- The happy end problem -- The man behind the theory : Frank Plumpton Ramsey -- Ramsey theory before Ramsey : Hilbert's theorem -- Ramsey theory before Ramsey : Schur's coloring solution of a colored problem and its generalizations -- Ramsey theory before Ramsey : Van der Waerden tells the story of creation -- Whose conjecture did Van der Waerden prove? Two lives between two wars : Issai Schur and Pierre Joseph Henry Baudet -- Monochromatic arithmetic progressions : life after Van der Waerden -- In search of Van der Waerden : the early years -- In search of Van der Waerden : the Nazi Leipzig, 1933-1945 -- In search of Van der Waerden : the postwar Amsterdam, 1945 -- In search of Van der Waerden : the unsettling years, 1946-1951 -- Monochromatic polygons in a 2-colored plane -- 3-colored plane, 2-colored space, and Ramsey sets -- Gallai's theorem -- Application of Baudet-Schur-Van der Waerden -- Application of Bergelson-Leibman's and Mordell-Faltings' theorems -- Solution of an Erdős problem : O'Donnell's theorem -- What if we had no choice? -- A glimpse into the future : chromatic number of the plane, theorems and conjectures -- Imagining the real, realizing the imaginary -- Two celebrated problems |
| Summary |
Focuses on problems involving colored objects, and results about the existence of certain exciting and unexpected properties that occur regardless of how these objects are colored. This book also addresses famous and exciting problems of Ramsey Theory, along with the history surrounding the discovery of Ramsey Theory |
| Bibliography |
Includes bibliographical references (pages 569-594) and indexes |
| Notes |
Print version record |
| Subject |
Ramsey theory.
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MATHEMATICS -- Graphic Methods.
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Biographie.
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Ebene.
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Farbe.
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Graphfärbung.
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Mathematiker.
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Mathematisches Problem.
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Ramsey-Theorie.
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Mathematics.
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Combinatorics.
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History of Mathematics.
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Mathematical Logic and Foundations.
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Ramsey theory.
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Ramsey theory
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Biografie
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Ebene
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Farbe
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Graphfärbung
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Mathematiker
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Mathematisches Problem
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Ramsey-Theorie
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| Genre/Form |
History
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| Form |
Electronic book
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| ISBN |
9780387746425 |
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0387746420 |
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1281830836 |
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9781281830838 |
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