The Triangle Free Process And The Ramsey Number R 3 K
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The Triangle Free Process And The Ramsey Number R 3 K
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Author : Gonzalo Fiz Pontiveros
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-04-03
The Triangle Free Process And The Ramsey Number R 3 K written by Gonzalo Fiz Pontiveros and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Education categories.
The areas of Ramsey theory and random graphs have been closely linked ever since Erdős's famous proof in 1947 that the “diagonal” Ramsey numbers R(k) grow exponentially in k. In the early 1990s, the triangle-free process was introduced as a model which might potentially provide good lower bounds for the “off-diagonal” Ramsey numbers R(3,k). In this model, edges of Kn are introduced one-by-one at random and added to the graph if they do not create a triangle; the resulting final (random) graph is denoted Gn,△. In 2009, Bohman succeeded in following this process for a positive fraction of its duration, and thus obtained a second proof of Kim's celebrated result that R(3,k)=Θ(k2/logk). In this paper the authors improve the results of both Bohman and Kim and follow the triangle-free process all the way to its asymptotic end.
Ramsey Theory
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Author : Xiaodong Xu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-06
Ramsey Theory written by Xiaodong Xu and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-06 with Mathematics categories.
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
Elementary Methods Of Graph Ramsey Theory
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Author : Yusheng Li
language : en
Publisher: Springer Nature
Release Date : 2022-09-16
Elementary Methods Of Graph Ramsey Theory written by Yusheng Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-16 with Mathematics categories.
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.
Building Bridges Ii
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Author : Imre Bárány
language : en
Publisher: Springer Nature
Release Date : 2020-02-04
Building Bridges Ii written by Imre Bárány and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-04 with Mathematics categories.
This volume collects together research and survey papers written by invited speakers of the conference celebrating the 70th birthday of László Lovász. The topics covered include classical subjects such as extremal graph theory, coding theory, design theory, applications of linear algebra and combinatorial optimization, as well as recent trends such as extensions of graph limits, online or statistical versions of classical combinatorial problems, and new methods of derandomization. László Lovász is one of the pioneers in the interplay between discrete and continuous mathematics, and is a master at establishing unexpected connections, “building bridges” between seemingly distant fields. His invariably elegant and powerful ideas have produced new subfields in many areas, and his outstanding scientific work has defined and shaped many research directions in the last 50 years. The 14 contributions presented in this volume, all of which are connected to László Lovász's areas of research, offer an excellent overview of the state of the art of combinatorics and related topics and will be of interest to experienced specialists as well as young researchers.
The Discrete Mathematical Charms Of Paul Erd S
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Author : Vašek Chvátal
language : en
Publisher: Cambridge University Press
Release Date : 2021-08-26
The Discrete Mathematical Charms Of Paul Erd S written by Vašek Chvátal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-26 with Computers categories.
A captivating introduction to key results of discrete mathematics through the work of Paul Erdős, blended with first-hand reminiscences.
Surveys In Combinatorics 2021
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Author : Konrad K. Dabrowski
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-24
Surveys In Combinatorics 2021 written by Konrad K. Dabrowski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.
These nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.
Degree Theory Of Immersed Hypersurfaces
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Author : Harold Rosenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Degree Theory Of Immersed Hypersurfaces written by Harold Rosenberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
The authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function.
Discrete Mathematics And Applications
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Author : Andrei M. Raigorodskii
language : en
Publisher: Springer Nature
Release Date : 2020-11-21
Discrete Mathematics And Applications written by Andrei M. Raigorodskii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-21 with Mathematics categories.
Advances in discrete mathematics are presented in this book with applications in theoretical mathematics and interdisciplinary research. Each chapter presents new methods and techniques by leading experts. Unifying interdisciplinary applications, problems, and approaches of discrete mathematics, this book connects topics in graph theory, combinatorics, number theory, cryptography, dynamical systems, finance, optimization, and game theory. Graduate students and researchers in optimization, mathematics, computer science, economics, and physics will find the wide range of interdisciplinary topics, methods, and applications covered in this book engaging and useful.
Localization For Thh Ku And The Topological Hochschild And Cyclic Homology Of Waldhausen Categories
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Author : Andrew J. Blumberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Localization For Thh Ku And The Topological Hochschild And Cyclic Homology Of Waldhausen Categories written by Andrew J. Blumberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
The authors resolve the longstanding confusion about localization sequences in $THH$ and $TC$ and establish a specialized devissage theorem.
The Mother Body Phase Transition In The Normal Matrix Model
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Author : Pavel M. Bleher
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
The Mother Body Phase Transition In The Normal Matrix Model written by Pavel M. Bleher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
In this present paper, the authors consider the normal matrix model with cubic plus linear potential.