At a Glance
204 Pages
23.39 x 15.6 x 1.27
Hardcover
$187.31
or 4 interest-free payments of $46.83 with
orAims to ship in 7 to 10 business days
Industry Reviews
"As we learn from the preface, [Ramsey Theory: Yesterday, Today and Tomorrow] grew out of an intentionally non-traditional conference on Ramsey theory. In accordance with that, the book itself is far from being a traditional textbook or reference book on the subject...We learn far more about the history of Ramsey theory than from other sources...the promise of discussing the future is fulfilled by a very extensive list of open problems contributed by numerous participants. Sometimes it is not even clear what the best way of asking a certain question is, and we are shown the raw form of the problem, just as we would if we participated at a conference...the book is undoubtedly a lot of fun. As one expects from a book on Ramsey theory, it is full of problems that are very easy to formulate, but terribly hard to solve...[the book] could well be used for a course using a seminar format, or for self-study by a graduate student familiarizing himself with the subject." -MAA Reviews
What This Book is About and How it Came into Being | p. vii |
Ramsey Theory Before Ramsey, Prehistory and Early History: An Essay in 13 Parts | p. 1 |
Overture | p. 1 |
David Hilbert's 1892 Cube Lemma | p. 2 |
The Issai Schur 1916 Theorem | p. 3 |
The Baudet-Schur-Van der Waerden 1927 Theorem | p. 7 |
The Generalized 1928 Schur Theorem | p. 8 |
The Frank Plumpton Ramsey Principle | p. 9 |
The Paul, Gjörgy, and Esther Happy End Problem | p. 11 |
Richard Rado's Regularity | p. 14 |
Density and Arithmetic Progressions | p. 17 |
The Tibor Gallai Theorem | p. 22 |
De Bruijn-Erdos's 1951 Compactness Theorem | p. 23 |
Khinchin's Small Book of Big Impact | p. 23 |
Long Live the Young Theory! | p. 24 |
References | p. 25 |
Eighty Years of Ramsey R(3, k) à and Counting! | p. 27 |
Basics | p. 27 |
George, Esther, Paul | p. 28 |
Erdos Magic | p. 29 |
An Erdos Gem | p. 30 |
Upper Bounds | p. 31 |
The Lovász Local Lemma | p. 33 |
Random Greedy Triangle-Free | p. 34 |
R(3, k) Resolved! | p. 35 |
Random Greedy Triangle-Free Redux | p. 36 |
Epilogue | p. 38 |
References | p. 38 |
Ramsey Numbers Involving Cycles | p. 41 |
Scope and Notation | p. 41 |
Two-Color Numbers Involving Cycles | p. 42 |
Cycles | p. 43 |
Cycles Versus Complete Graphs | p. 44 |
Cycles Versus Wheels | p. 46 |
Cycles Versus Books | p. 47 |
Cycles Versus Other Graphs | p. 49 |
Multicolor Numbers for Cycles | p. 50 |
Three Colors | p. 50 |
More Colors | p. 53 |
Cycles Versus Other Graphs | p. 54 |
Hypergraph Numbers for Cycles | p. 55 |
References | p. 56 |
On the Function of Erdos and Rogers | p. 63 |
Introduction | p. 63 |
The Most Restrictive Case | p. 64 |
Proof of fs,s+1(n)≤0(n1-1/0(s4log s))[1] | p. 65 |
Proof of ¿(n½)≤fs,s+1(n) for s≥2[2] | p. 67 |
Proof of fs,s+1(n) ≤0(n2/3) for s≥2 [4] | p. 67 |
General Bounds | p. 69 |
Proof of ¿(nak(s))≤fs,s+k(n) [14, 15] | p. 71 |
Sketch of the Proof of fs,s+k(n)≤0(n((k+1)/(2k+1))+¿) for s≥s0 = s0(¿, k) [4] | p. 73 |
Concluding Remarks | p. 75 |
References | p. 75 |
Large Monochromatic Components in Edge Colorings of Graphs: A Survey | p. 77 |
Introduction | p. 77 |
A Remark of Erdos and Rado and Its Extension | p. 77 |
Colorings from Affine Planes | p. 78 |
Extending Colorings by Substitutions | p. 79 |
2-Colorings | p. 79 |
Type of Spanning Trees, Connectivity, Diameter | p. 79 |
Gallai-Colorings: Substitutions to 2-Colorings | p. 82 |
Multicolorings: Basic Results and Proof Methods | p. 83 |
Complete Bipartite Graphs: Counting Double Stars | p. 83 |
Fractional Transversals: Füredi's Method | p. 85 |
Fine Tuning | p. 85 |
When Both Methods Work: Local Colorings | p. 86 |
Hypergraphs | p. 88 |
Multicolorings: Type of Components | p. 89 |
Components with Large Matching | p. 89 |
Double Stars | p. 90 |
Variations | p. 90 |
Vertex-Coverings by Components | p. 91 |
Coloring by Group Elements | p. 91 |
Coloring Geometric Graphs | p. 91 |
Coloring Noncomplete Graphs | p. 92 |
References | p. 94 |
Szlam's Lemma: Mutant Offspring of a Euclidean Ramsey Problem from 1973, with Numerous Applications | p. 97 |
1973: A Volcano Erupts | p. 97 |
Some Definitions and More Background | p. 98 |
What Happened to the Rather Red Coloring Problem from 1973? | p. 101 |
Distance Graphs | p. 102 |
Szlam's Lemma, a Connection Between Rather Red Colorings and Chromatic Numbers | p. 104 |
van der Waerden Numbers, Cyclic van der Waerden Numbers, and a Lower Bound on Them Both | p. 107 |
References | p. 112 |
Open Problems in Euclidean Ramsey Theory | p. 115 |
Introduction | p. 115 |
Ramsey Sets | p. 117 |
Unit Distance Graphs | p. 117 |
More General Distance Graphs | p. 119 |
References | p. 119 |
Chromatic Number of the Plane & Its Relatives, History, Problems and Results: An Essay in 11 Parts | p. 121 |
The Problem | p. 121 |
The History | p. 124 |
Polychromatic Number of the Plane & Results Near the Lower Bound | p. 135 |
De Bruijn-Erdos Reduction to Finite Sets and Results Near the Lower Bound | p. 138 |
Polychromatic Number of the Plane & Results Near the Upper Bound | p. 141 |
Continum of 6-Colorings of the Plane | p. 144 |
Chromatic Number of the Plane in Special Circumstances | p. 148 |
Colored Space | p. 149 |
Rational Coloring | p. 151 |
Axioms of Set Theory and the Chromatic Number of Graphs | p. 153 |
Predicting the Future | p. 156 |
References | p. 157 |
Euclidean Distance Graphs on the Rational Points | p. 163 |
Definitions | p. 163 |
The Search for ¿(Rn, 1) Leads to the Search for ¿(Qn, 1) | p. 164 |
Distances Other Than 1? | p. 167 |
Problems | p. 172 |
References | p. 174 |
Open Problems Session | p. 177 |
Problems Submitted | p. 179 |
Problems Submitted | p. 180 |
Problems on Topological Stability of Chromatic Numbers Submitted | p. 182 |
Problem on the Gallai-Ramsey Structure, Submitted | p. 183 |
Problems Involving Triangles, Submitted | p. 185 |
Problems on Chromatic Number of the Plane and Its Relatives, Submitted | p. 189 |
Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780817680916
ISBN-10: 0817680918
Series: Progress in Mathematics
Published: 5th November 2010
Format: Hardcover
Language: English
Number of Pages: 204
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: US
Dimensions (cm): 23.39 x 15.6 x 1.27
Weight (kg): 0.46
Shipping
Standard Shipping | Express Shipping | |
---|---|---|
Metro postcodes: | $9.99 | $14.95 |
Regional postcodes: | $9.99 | $14.95 |
Rural postcodes: | $9.99 | $14.95 |
How to return your order
At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.
Additional postage charges may be applicable.
Defective items
If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.
For more info please visit our Help Centre.
You Can Find This Book In
Introduction to Cryptography with Mathematical Foundations and Computer Implementations
Discrete Mathematics and Its Applications
Paperback
RRP $120.00
$101.25
OFF