عنوان

Ramsey theory :

(Number (ISBN

3110576635

(Number (ISBN

3110576708

(Number (ISBN

9783110576634

(Number (ISBN

9783110576702

Erroneous ISBN

3110576511

Erroneous ISBN

9783110576511

Title Proper

Ramsey theory :

General Material Designation

[Book]

Other Title Information

unsolved problems and results /

First Statement of Responsibility

Xiaodong Xu, Meilian Liang, Haipeng Luo.

Place of Publication, Distribution, etc.

Boston :

Name of Publisher, Distributor, etc.

De Gruyter,

Date of Publication, Distribution, etc.

[2018]

Specific Material Designation and Extent of Item

1 online resource

Text of Note

Includes bibliographical references and index.

Text of Note

Some definitions and notations -- Ramsey theory -- Bi-color diagonal classical Ramsey numbers -- Paley graphs and lower bounds for r(k; k) -- Bi-color o-diagonal classical Ramsey numbers -- Multicolor classical Ramsey numbers -- Generalized Ramsey numbers -- Folkman numbers -- The Erdos-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 -- Epilogue.

0

Text of Note

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.

Title

Ramsey theory.

International Standard Book Number

3110576511

Combinatorial analysis.

Graph theory.

Ramsey theory.

Combinatorial analysis.

Graph theory.

MATHEMATICS-- General.

Ramsey theory.

MAT-- 000000

Number

Edition

Class number

Book number

Xu, Xiaodong, (Physicist)

Liang, Meilian

Luo, Haipeng

Date of Transaction

20200823095837.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y