Elementary Methods Of Graph Ramsey Theory

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Elementary Methods of Graph Ramsey Theory

Yusheng Li,Qizhong Lin
Elementary Methods of Graph Ramsey Theory Book PDF

Author : Yusheng Li,Qizhong Lin
Publisher : Springer Nature
Page : 349 pages
File Size : 51,8 Mb
Release : 2022-09-16
Category : Mathematics
ISBN : 9783031127625

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Elementary Methods of Graph Ramsey Theory by Yusheng Li,Qizhong Lin Pdf

This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey theory, and related fields, as the included contents allow the text to be used in seminars. It is structured in thirteen chapters which are application-focused and largely independent, enabling readers to target specific topics and information to focus their study. The first chapter includes a true beginner’s overview of elementary examples in graph Ramsey theory mainly using combinatorial methods. The following chapters progress through topics including the probabilistic methods, algebraic construction, regularity method, but that's not all. Many related interesting topics are also included in this book, such as the disproof for a conjecture of Borsuk on geometry, intersecting hypergraphs, Turán numbers and communication channels, etc.

Ramsey Theory

Ronald L. Graham,Bruce L. Rothschild,Joel H. Spencer
Ramsey Theory Book PDF

Author : Ronald L. Graham,Bruce L. Rothschild,Joel H. Spencer
Publisher : John Wiley & Sons
Page : 230 pages
File Size : 42,8 Mb
Release : 1991-01-16
Category : Mathematics
ISBN : 0471500461

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Ramsey Theory by Ronald L. Graham,Bruce L. Rothschild,Joel H. Spencer Pdf

Praise for the First Edition "Anyone interested in getting an introduction to Ramsey theorywill find this illuminating..." --MAA Reviews Covering all the major concepts, proofs, and theorems, theSecond Edition of Ramsey Theory is the ultimate guideto understanding every aspect of Shelah's proof, as well asthe original proof of van der Waerden. The book offers a historicalperspective of Ramsey's fundamental paper from 1930 andErdos' and Szekeres' article from 1935, while placingthe various theorems in the context of T. S. Motzkin'sthought on the subject of "Complete Disorder isImpossible." Ramsey Theory, Second Edition includes new and excitingcoverage of Graph Ramsey Theory and Euclidean Ramsey Theory andalso relates Ramsey Theory to other areas in discrete mathematics.In addition, the book features the unprovability results of Parisand Harrington and the methods from topological dynamics pioneeredby Furstenburg. Featuring worked proofs and outside applications, RamseyTheory, Second Edition addresses: * Ramsey and density theorems on both broad and meticulousscales * Extentions and implications of van der Waerden's Theorem,the Hales-Jewett Theorem, Roth's Theorem, Rado'sTheorem, Szemeredi's Theorem, and the Shelah Proof * Regular homogeneous and nonhomogeneous systems andequations * Special cases and broader interdisciplinary applications ofRamsey Theory principles An invaluable reference for professional mathematicians workingin discrete mathematics, combinatorics, and algorithms, RamseyTheory, Second Edition is the definitive work on thesubject.

Star-Critical Ramsey Numbers for Graphs

Mark R. Budden
Star Critical Ramsey Numbers for Graphs Book PDF

Author : Mark R. Budden
Publisher : Springer Nature
Page : 102 pages
File Size : 42,6 Mb
Release : 2023-05-13
Category : Mathematics
ISBN : 9783031299810

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Star-Critical Ramsey Numbers for Graphs by Mark R. Budden Pdf

This text is a comprehensive survey of the literature surrounding star-critical Ramsey numbers. First defined by Jonelle Hook in her 2010 dissertation, these numbers aim to measure the sharpness of the corresponding Ramsey numbers by determining the minimum number of edges needed to be added to a critical graph for the Ramsey property to hold. Despite being in its infancy, the topic has gained significant attention among Ramsey theorists. This work provides researchers and students with a resource for studying known results and their complete proofs. It covers typical results, including multicolor star-critical Ramsey numbers for complete graphs, trees, cycles, wheels, and n-good graphs, among others. The proofs are streamlined and, in some cases, simplified, with a few new results included. The book also explores the connection between star-critical Ramsey numbers and deleted edge numbers, which focus on destroying the Ramsey property by removing edges. The book concludes with open problems and conjectures for researchers to consider, making it a valuable resource for those studying the field of star-critical Ramsey numbers.

Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

Mauro Di Nasso,Isaac Goldbring,Martino Lupini
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory Book PDF

Author : Mauro Di Nasso,Isaac Goldbring,Martino Lupini
Publisher : Springer
Page : 206 pages
File Size : 50,9 Mb
Release : 2019-05-23
Category : Mathematics
ISBN : 9783030179564

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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory by Mauro Di Nasso,Isaac Goldbring,Martino Lupini Pdf

The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.

Combinatorial Optimization and Applications

Weili Wu,Jianxiong Guo
Combinatorial Optimization and Applications Book PDF

Author : Weili Wu,Jianxiong Guo
Publisher : Springer Nature
Page : 505 pages
File Size : 42,5 Mb
Release : 2024-01-09
Category : Computers
ISBN : 9783031496141

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Combinatorial Optimization and Applications by Weili Wu,Jianxiong Guo Pdf

The two-volume set LNCS 14461 and LNCS 14462 constitutes the refereed proceedings of the 17th International Conference on Combinatorial Optimization and Applications, COCOA 2023, held in Hawaii, HI, USA, during December 15–17, 2023. The 73 full papers included in the proceedings were carefully reviewed and selected from 117 submissions. They were organized in topical sections as follows: Part I: Optimization in graphs; scheduling; set-related optimization; applied optimization and algorithm; Graph planer and others; Part II: Modeling and algorithms; complexity and approximation; combinatorics and computing; optimization and algorithms; extreme graph and others; machine learning, blockchain and others.

Rudiments of Ramsey Theory

Ronald L. Graham
Rudiments of Ramsey Theory Book PDF

Author : Ronald L. Graham
Publisher : American Mathematical Soc.
Page : 74 pages
File Size : 55,7 Mb
Release : 1981-12-31
Category : Mathematics
ISBN : 9780821816967

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Rudiments of Ramsey Theory by Ronald L. Graham Pdf

It is no exaggeration to say that over the past several decades there has been a veritable explosion of activity in the general field of combinatorics. Ramsey theory, in particular, has shown remarkable growth. This book gives a picture of the state of the art of Ramsey theory at the time of Graham's CBMS lectures. In keeping with the style of the lectures, the exposition is informal. However, complete proofs are given for most of the basic results presented. In addition, many useful results may be found in the exercises and problems. Loosely speaking, Ramsey theory is the branch of combinatorics that deals with structures that are preserved under partitions. Typically, one looks at the following kind of question: If a particular structure (e.g., algebraic, combinatorial or geometric) is arbitrarily partitioned into finitely many classes, what kinds of substructures must always remain intact in at least one of the classes? At the time of these lectures, a number of spectacular advances had been made in the field of Ramsey theory. These include: the work of Szemeredi and Furstenberg settling the venerable conjecture of Erdos and Turan, the Nesetril-Rodl theorems on induced Ramsey properties, the results of Paris and Harrington on ``large'' Ramsey numbers and undecidability in first-order Peano arithmetic, Deuber's solution to the old partition regularity conjecture of Rado, Hindman's surprising generalization of Schur's theorem, and the resolution of Rota's conjecture on Ramsey's theorem for vector spaces by Graham, Leeb and Rothschild. It has also become apparent that the ideas and techniques of Ramsey theory span a rather broad range of mathematical areas, interacting in essential ways with parts of set theory, graph theory, combinatorial number theory, probability theory, analysis and even theoretical computer science. These lecture notes lay out the foundation on which much of this work is based. Relatively little specialized mathematical background is required for this book. It should be accessible to upper division students.

Ramsey Theory

Xiaodong Xu,Meilian Liang,Haipeng Luo
Ramsey Theory Book PDF

Author : Xiaodong Xu,Meilian Liang,Haipeng Luo
Publisher : Walter de Gruyter GmbH & Co KG
Page : 190 pages
File Size : 42,5 Mb
Release : 2018-08-06
Category : Mathematics
ISBN : 9783110576702

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Ramsey Theory by Xiaodong Xu,Meilian Liang,Haipeng Luo Pdf

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. Contents Some definitions and notations Ramsey theory Bi-color diagonal classical Ramsey numbers Paley graphs and lower bounds for R(k, k) Bi-color off-diagonal classical Ramsey numbers Multicolor classical Ramsey numbers Generalized Ramsey numbers Folkman numbers The 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

An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics

Matthew Katz,Jan Reimann
An Introduction to Ramsey Theory Fast Functions Infinity and Metamathematics Book PDF

Author : Matthew Katz,Jan Reimann
Publisher : American Mathematical Soc.
Page : 207 pages
File Size : 45,5 Mb
Release : 2018-10-03
Category : Combinatorial analysis
ISBN : 9781470442903

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An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics by Matthew Katz,Jan Reimann Pdf

This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explored are Ramsey's theorem for graphs and hypergraphs, van der Waerden's theorem on arithmetic progressions, infinite ordinals and cardinals, fast growing functions, logic and provability, Gödel incompleteness, and the Paris-Harrington theorem. Quoting from the book, “There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.”

Rudiments of Ramsey Theory

Ron Graham, Steve Butler
Rudiments of Ramsey Theory Book PDF

Author : Ron Graham, Steve Butler
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 43,8 Mb
Release : 2015-10-01
Category : Combinatorial analysis
ISBN : 9780821841563

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Rudiments of Ramsey Theory by Ron Graham, Steve Butler Pdf

In every sufficiently large structure which has been partitioned there will always be some well-behaved structure in one of the parts. This takes many forms. For example, colorings of the integers by finitely many colors must have long monochromatic arithmetic progressions (van der Waerden's theorem); and colorings of the edges of large graphs must have monochromatic subgraphs of a specified type (Ramsey's theorem). This book explores many of the basic results and variations of this theory. Since the first edition of this book there have been many advances in this field. In the second edition the authors update the exposition to reflect the current state of the art. They also include many pointers to modern results. A co-publication of the AMS and CBMS.

Ramsey Theory

Alexander Soifer
Ramsey Theory Book PDF

Author : Alexander Soifer
Publisher : Springer Science & Business Media
Page : 190 pages
File Size : 50,7 Mb
Release : 2010-10-29
Category : Mathematics
ISBN : 9780817680923

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Ramsey Theory by Alexander Soifer Pdf

This book explores the theory’s history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike.

Topics in Gallai-Ramsey Theory

Colton Magnant,Pouria Salehi Nowbandegani
Topics in Gallai Ramsey Theory Book PDF

Author : Colton Magnant,Pouria Salehi Nowbandegani
Publisher : Springer Nature
Page : 110 pages
File Size : 55,9 Mb
Release : 2020-07-04
Category : Mathematics
ISBN : 9783030488970

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Topics in Gallai-Ramsey Theory by Colton Magnant,Pouria Salehi Nowbandegani Pdf

This book explores topics in Gallai-Ramsey theory, which looks into whether rainbow colored subgraphs or monochromatic subgraphs exist in a sufficiently large edge-colored complete graphs. A comprehensive survey of all known results with complete references is provided for common proof methods. Fundamental definitions and preliminary results with illustrations guide readers to comprehend recent innovations. Complete proofs and influential results are discussed with numerous open problems and conjectures. Researchers and students with an interest in edge-coloring, Ramsey Theory, and colored subgraphs will find this book a valuable guide for entering Gallai-Ramsey Theory.

Ramsey Theory on the Integers

Bruce M. Landman, Aaron Robertson
Ramsey Theory on the Integers Book PDF

Author : Bruce M. Landman, Aaron Robertson
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 54,9 Mb
Release : 2014-11-10
Category : Mathematics
ISBN : 9780821898673

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Ramsey Theory on the Integers by Bruce M. Landman, Aaron Robertson Pdf

Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems. For this new edition, several sections have been added and others have been significantly updated. Among the newly introduced topics are: rainbow Ramsey theory, an "inequality" version of Schur's theorem, monochromatic solutions of recurrence relations, Ramsey results involving both sums and products, monochromatic sets avoiding certain differences, Ramsey properties for polynomial progressions, generalizations of the Erdős-Ginzberg-Ziv theorem, and the number of arithmetic progressions under arbitrary colorings. Many new results and proofs have been added, most of which were not known when the first edition was published. Furthermore, the book's tables, exercises, lists of open research problems, and bibliography have all been significantly updated. This innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subject. This breakthrough book will engage students, teachers, and researchers alike.

Ramsey Theory for Discrete Structures

Hans Jürgen Prömel
Ramsey Theory for Discrete Structures Book PDF

Author : Hans Jürgen Prömel
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 47,7 Mb
Release : 2013-12-04
Category : Mathematics
ISBN : 9783319013152

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Ramsey Theory for Discrete Structures by Hans Jürgen Prömel Pdf

This monograph covers some of the most important developments in Ramsey theory from its beginnings in the early 20th century via its many breakthroughs to recent important developments in the early 21st century. The book first presents a detailed discussion of the roots of Ramsey theory before offering a thorough discussion of the role of parameter sets. It presents several examples of structures that can be interpreted in terms of parameter sets and features the most fundamental Ramsey-type results for parameter sets: Hales-Jewett's theorem and Graham-Rothschild1s Ramsey theorem as well as their canonical versions and several applications. Next, the book steps back to the most basic structure, to sets. It reviews classic results as well as recent progress on Ramsey numbers and the asymptotic behavior of classical Ramsey functions. In addition, it presents product versions of Ramsey's theorem, a combinatorial proof of the incompleteness of Peano arithmetic, provides a digression to discrepancy theory and examines extensions of Ramsey's theorem to larger cardinals. The next part of the book features an in-depth treatment of the Ramsey problem for graphs and hypergraphs. It gives an account on the existence of sparse and restricted Ramsey theorem's using sophisticated constructions as well as probabilistic methods. Among others it contains a proof of the induced Graham-Rothschild theorem and the random Ramsey theorem. The book closes with a chapter on one of the recent highlights of Ramsey theory: a combinatorial proof of the density Hales-Jewett theorem. This book provides graduate students as well as advanced researchers with a solid introduction and reference to the field.

Mathematics of Ramsey Theory

Jaroslav Nesetril,Vojtech Rödl
Mathematics of Ramsey Theory Book PDF

Author : Jaroslav Nesetril,Vojtech Rödl
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642729058

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Mathematics of Ramsey Theory by Jaroslav Nesetril,Vojtech Rödl Pdf

One of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partitions. The general philosophy is reflected by its interdisciplinary character. The ideas of Ramsey theory are shared by logicians, set theorists and combinatorists, and have been successfully applied in other branches of mathematics. The whole subject is quickly developing and has some new and unexpected applications in areas as remote as functional analysis and theoretical computer science. This book is a homogeneous collection of research and survey articles by leading specialists. It surveys recent activity in this diverse subject and brings the reader up to the boundary of present knowledge. It covers virtually all main approaches to the subject and suggests various problems for individual research.

Graph Theory

Ralucca Gera,Stephen Hedetniemi,Craig Larson
Graph Theory Book PDF

Author : Ralucca Gera,Stephen Hedetniemi,Craig Larson
Publisher : Springer
Page : 291 pages
File Size : 40,6 Mb
Release : 2016-10-19
Category : Mathematics
ISBN : 9783319319407

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Graph Theory by Ralucca Gera,Stephen Hedetniemi,Craig Larson Pdf

This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician will find the overall exposition engaging and enlightening. Each chapter, presented in a story-telling style, includes more than a simple collection of results on a particular topic. Each contribution conveys the history, evolution, and techniques used to solve the authors’ favorite conjectures and open problems, enhancing the reader’s overall comprehension and enthusiasm. The editors were inspired to create these volumes by the popular and well attended special sessions, entitled “My Favorite Graph Theory Conjectures," which were held at the winter AMS/MAA Joint Meeting in Boston (January, 2012), the SIAM Conference on Discrete Mathematics in Halifax (June,2012) and the winter AMS/MAA Joint meeting in Baltimore(January, 2014). In an effort to aid in the creation and dissemination of open problems, which is crucial to the growth and development of a field, the editors requested the speakers, as well as notable experts in graph theory, to contribute to these volumes.