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Ramsey Theory

Part of the Progress in Mathematics Book Series (volume 285)

Editors: Soifer, Alexander

DOI: 10.1007/978-0-8176-8092-3

ISBN: 978-0-8176-8091-6

Publisher: Birkhäuser Boston - Springer Journals

Oct 12, 2011

1 - 10 of 10 Chapters

LitStream

Chapter 1Ramsey Theory Before Ramsey, Prehistory and Early History: An Essay in 13 Parts

Soifer, Alexander

Pages: 1 –26

[How does a new theory emerge? It usually manifests itself in the older and established areas of mathematics. Gradually a critical mass of results appears, prompting a realization that what we have is a new identifiable field of mathematical thought, with its own set of problems and methods. As a...
LitStream

Chapter 2Eighty Years of RamseyR(3, k)…and Counting!

Spencer, Joel

Pages: 27 –39

[How frequently does an intriguing problem come up over lunchtime, only to have it solved the next morning? How many mathematical problems are seemingly intractable? Decades go by without a hint of progress. What a delight when a problem is worked on over many many years with progress occurring...
LitStream

Chapter 3Ramsey Numbers Involving Cycles

Radziszowski, Stanisław P.

Pages: 41 –62

[There is a vast amount of literature on Ramsey-type problems starting in 1930 with the original paper of Ramsey [Ram]. Graham, Rothschild and Spencer in their book, Ramsey Theory [GRS] and Soifer in the 2009 The Mathematical Coloring Book, Mathematics of Coloring and the Colorful Life of Its...
LitStream

Chapter 4On the Function of Erdős and Rogers

Dudek, Andrzej; Rödl, Vojtěch

Pages: 63 –76

[In 1930, Frank Ramsey published a seminal paper “On a problem of formal logic”[13] beginning a new area of research known today as Ramsey theory (for a comprehensive introduction to Ramsey theory see, e.g.,[9]).]
LitStream

Chapter 5Large Monochromatic Components in Edge Colorings of Graphs: A Survey

Gyárfás, András

Pages: 77 –96

[The aim of this survey is to summarize an area of combinatorics that lies on the border of several areas: Ramsey theory, resolvable block designs, factorizations, fractional matchings and coverings, and partition covers.]
LitStream

Chapter 6Szlam’s Lemma: Mutant Offspring of a Euclidean Ramsey Problem from 1973, with Numerous Applications

Burkert, Jeffrey; Johnson, Peter

Pages: 97 –113

[If you treasure semantic precision, you might name the volcano that erupted (figuratively speaking!) in 1973: Coloring Problems in Geometrically Defined Hypergraphs.]
LitStream

Chapter 7Open Problems in Euclidean Ramsey Theory

Graham, Ron; Tressler, Eric

Pages: 115 –120

[Ramsey theory is the study of structure that must exist in a system, most typically after it has been partitioned.]
LitStream

Chapter 8Chromatic Number of the Plane & Its Relatives, History, Problems and Results: An Essay in 11 Parts

Soifer, Alexander

Pages: 121 –161

[In August 1987 I attended an inspiring talk by Paul Halmos at Chapman College in Orange, California. It was entitled “Some Problems You Can Solve, and Some You Cannot.” This problem was an example of a problem “you cannot solve.”]
LitStream

Chapter 9Euclidean Distance Graphs on the Rational Points

Johnson, Peter

Pages: 163 –176

[Throughout, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{Z}$$...
LitStream

Chapter 10Open Problems Session

Soifer, Alexander

Pages: 177 –189

[During the workshop Ramsey Theory Yesterday, Today and Tomorrow at Rutgers University on May 27-29, 2009, I offered a Problem Posing Session. All 30 participants of the workshop attended the session, and almost everyone came to the board and posed favorite open problems. The session was...

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