Proof Of The 1 Factorization And Hamilton Decomposition Conjectures

Author : Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 49,6 Mb
Release : 2016-10-05
Category : 1-factorization
ISBN : 9781470420253

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Proof of the 1-Factorization and Hamilton Decomposition Conjectures by Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown Pdf

In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D≥2⌈n/4⌉−1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, χ′(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D≥⌊n/2⌋. Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree δ≥n/2. Then G contains at least regeven(n,δ)/2≥(n−2)/8 edge-disjoint Hamilton cycles. Here regeven(n,δ) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree δ. (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case δ=⌈n/2⌉ of (iii) answer questions of Nash-Williams from 1970. All of the above bounds are best possible.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,5 Mb
Release : 2016-10-01
Category : Electronic
ISBN : 147043508X

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Proof of the 1-Factorization and Hamilton Decomposition Conjectures by Anonim Pdf

Author : Jaroslav Nešetřil,Marco Pellegrini
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 48,8 Mb
Release : 2014-01-18
Category : Mathematics
ISBN : 9788876424755

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The Seventh European Conference on Combinatorics, Graph Theory and Applications by Jaroslav Nešetřil,Marco Pellegrini Pdf

In the tradition of EuroComb'01 (Barcelona), Eurocomb'03 (Prague), EuroComb'05 (Berlin), Eurocomb'07 (Seville), Eurocomb'09 (Bordeaux), and Eurocomb'11 (Budapest), this volume covers recent advances in combinatorics and graph theory including applications in other areas of mathematics, computer science and engineering. Topics include, but are not limited to: Algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, ordered sets, random methods, topological combinatorics.

Author : Reinhard Diestel
Publisher : Springer-Verlag, © Reinhard Diestel
Page : 447 pages
File Size : 53,9 Mb
Release : 2017-02-01
Category : Electronic
ISBN : 9783961340057

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Graph Theory by Reinhard Diestel Pdf

Professional electronic edition available from http://diestel-graph-theory.com/professional.html This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. New in this 5th edition: Sections on tangles and tree-width, on tree packing and covering, and on topological spaces as inverse limits of finite graphs. Several new proofs of classical theorems. Many new exercises. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.” Acta Scientiarum Mathematicarum "Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity." Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory.” Bulletin of the Institute of Combinatorics and its Applications “Succeeds dramatically… a hell of a good book.” MAA Reviews “A highlight of the book is what is by far the best account in print of the Seymour-Robertson theory of graph minors.” Mathematika “…like listening to someone explain mathematics.” Bulletin of the AMS

Author : Jaroslav Nešetřil,Guillem Perarnau,Juanjo Rué,Oriol Serra
Publisher : Springer Nature
Page : 875 pages
File Size : 40,5 Mb
Release : 2021-08-23
Category : Mathematics
ISBN : 9783030838232

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Extended Abstracts EuroComb 2021 by Jaroslav Nešetřil,Guillem Perarnau,Juanjo Rué,Oriol Serra Pdf

This book collects the extended abstracts of the accepted contributions to EuroComb21. A similar book is published at every edition of EuroComb (every two years since 2001) collecting the most recent advances in combinatorics, graph theory, and related areas. It has a wide audience in the areas, and the papers are used and referenced broadly.

Author : Ralucca Gera,Teresa W. Haynes,Stephen T. Hedetniemi
Publisher : Springer
Page : 281 pages
File Size : 44,9 Mb
Release : 2018-10-26
Category : Mathematics
ISBN : 9783319976860

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Graph Theory by Ralucca Gera,Teresa W. Haynes,Stephen T. Hedetniemi Pdf

This second volume in a two-volume series provides an extensive collection of conjectures and open problems in graph theory. It is designed for both graduate students and established researchers in discrete mathematics who are searching for research ideas and references. Each chapter provides more than a simple collection of results on a particular topic; it captures the reader’s interest with techniques that worked and failed in attempting to solve particular conjectures. The history and origins of specific conjectures and the methods of researching them are also included throughout this volume. Students and researchers can discover how the conjectures have evolved and the various approaches that have been used in an attempt to solve them. An annotated glossary of nearly 300 graph theory parameters, 70 conjectures, and over 600 references is also included in this volume. This glossary provides an understanding of parameters beyond their definitions and enables readers to discover new ideas and new definitions in graph theory. The editors were inspired to create this series of volumes by the popular and well-attended special sessions entitled “My Favorite Graph Theory Conjectures,” which they organized at past AMS meetings. These sessions were held at the winter AMS/MAA Joint Meeting in Boston, January 2012, the SIAM Conference on Discrete Mathematics in Halifax in June 2012, as well as the winter AMS/MAA Joint Meeting in Baltimore in January 2014, at which many of the best-known graph theorists spoke. In an effort to aid in the creation and dissemination of conjectures and open problems, which is crucial to the growth and development of this field, the editors invited these speakers, as well as other experts in graph theory, to contribute to this series.

Author : Gary Chartrand,Heather Jordon,Vincent Vatter,Ping Zhang
Publisher : CRC Press
Page : 365 pages
File Size : 47,8 Mb
Release : 2024-01-23
Category : Mathematics
ISBN : 9781003801085

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Graphs & Digraphs by Gary Chartrand,Heather Jordon,Vincent Vatter,Ping Zhang Pdf

Graphs & Digraphs, Seventh Edition masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. This classic text, widely popular among students and instructors alike for decades, is thoroughly streamlined in this new, seventh edition, to present a text consistent with contemporary expectations. Changes and updates to this edition include: A rewrite of four chapters from the ground up Streamlining by over a third for efficient, comprehensive coverage of graph theory Flexible structure with foundational Chapters 1–6 and customizable topics in Chapters 7–11 Incorporation of the latest developments in fundamental graph theory Statements of recent groundbreaking discoveries, even if proofs are beyond scope Completely reorganized chapters on traversability, connectivity, coloring, and extremal graph theory to reflect recent developments The text remains the consummate choice for an advanced undergraduate level or introductory graduate-level course exploring the subject’s fascinating history, while covering a host of interesting problems and diverse applications. Our major objective is to introduce and treat graph theory as the beautiful area of mathematics we have always found it to be. We have striven to produce a reader-friendly, carefully written book that emphasizes the mathematical theory of graphs, in all their forms. While a certain amount of mathematical maturity, including a solid understanding of proof, is required to appreciate the material, with a small number of exceptions this is the only pre-requisite. In addition, owing to the exhilarating pace of progress in the field, there have been countless developments in fundamental graph theory ever since the previous edition, and many of these discoveries have been incorporated into the book. Of course, some of the proofs of these results are beyond the scope of the book, in which cases we have only included their statements. In other cases, however, these new results have led us to completely reorganize our presentation. Two examples are the chapters on coloring and extremal graph theory.

Author : Karin R Saoub
Publisher : CRC Press
Page : 394 pages
File Size : 43,5 Mb
Release : 2021-03-17
Category : Mathematics
ISBN : 9780429779879

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Graph Theory by Karin R Saoub Pdf

Graph Theory: An Introduction to Proofs, Algorithms, and Applications Graph theory is the study of interactions, conflicts, and connections. The relationship between collections of discrete objects can inform us about the overall network in which they reside, and graph theory can provide an avenue for analysis. This text, for the first undergraduate course, will explore major topics in graph theory from both a theoretical and applied viewpoint. Topics will progress from understanding basic terminology, to addressing computational questions, and finally ending with broad theoretical results. Examples and exercises will guide the reader through this progression, with particular care in strengthening proof techniques and written mathematical explanations. Current applications and exploratory exercises are provided to further the reader’s mathematical reasoning and understanding of the relevance of graph theory to the modern world. Features The first chapter introduces graph terminology, mathematical modeling using graphs, and a review of proof techniques featured throughout the book The second chapter investigates three major route problems: eulerian circuits, hamiltonian cycles, and shortest paths. The third chapter focuses entirely on trees – terminology, applications, and theory. Four additional chapters focus around a major graph concept: connectivity, matching, coloring, and planarity. Each chapter brings in a modern application or approach. Hints and Solutions to selected exercises provided at the back of the book. Author Karin R. Saoub is an Associate Professor of Mathematics at Roanoke College in Salem, Virginia. She earned her PhD in mathematics from Arizona State University and BA from Wellesley College. Her research focuses on graph coloring and on-line algorithms applied to tolerance graphs. She is also the author of A Tour Through Graph Theory, published by CRC Press.

Author : Bo’az Klartag
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 43,6 Mb
Release : 2017-09-25
Category : Curvature
ISBN : 9781470425425

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Needle Decompositions in Riemannian Geometry by Bo’az Klartag Pdf

The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.

Author : Charles Fefferman,James P. Lee-Thorp,M. I. Weinstein
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 46,8 Mb
Release : 2017-04-25
Category : Dirac equation
ISBN : 9781470423230

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Topologically Protected States in One-Dimensional Systems by Charles Fefferman,James P. Lee-Thorp,M. I. Weinstein Pdf

The authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They then show that the introduction of an ``edge'', via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized ``edge states''. These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.

Author : Allan Bickle
Publisher : American Mathematical Soc.
Page : 336 pages
File Size : 52,9 Mb
Release : 2020-03-10
Category : Education
ISBN : 9781470453428

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Fundamentals of Graph Theory by Allan Bickle Pdf

Graph theory is a fascinating and inviting branch of mathematics. Many problems are easy to state and have natural visual representations, inviting exploration by new students and professional mathematicians. The goal of this textbook is to present the fundamentals of graph theory to a wide range of readers. The book contains many significant recent results in graph theory, presented using up-to-date notation. The author included the shortest, most elegant, most intuitive proofs for modern and classic results while frequently presenting them in new ways. Major topics are introduced with practical applications that motivate their development, and which are illustrated with examples that show how to apply major theorems in practice. This includes the process of finding a brute force solution (case-checking) when an elegant solution is not apparent. With over 1200 exercises, internet resources (e.g., the OEIS for counting problems), helpful appendices, and a detailed guide to different course outlines, this book provides a versatile and convenient tool for the needs of instructors at a large variety of institutions.

Author : Anders Claesson,Mark Dukes,Sergey Kitaev,David Manlove,Kitty Meeks
Publisher : Cambridge University Press
Page : 451 pages
File Size : 54,7 Mb
Release : 2017-06-30
Category : Mathematics
ISBN : 9781108413138

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Surveys in Combinatorics 2017 by Anders Claesson,Mark Dukes,Sergey Kitaev,David Manlove,Kitty Meeks Pdf

This book includes nine articles representing a timely snapshot of the state of the art in the different areas of combinatorics.

Author : Akinari Hoshi,Aiichi Yamasaki
Publisher : American Mathematical Soc.
Page : 215 pages
File Size : 42,8 Mb
Release : 2017-07-13
Category : Affine algebraic groups
ISBN : 9781470424091

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Rationality Problem for Algebraic Tori by Akinari Hoshi,Aiichi Yamasaki Pdf

The authors give the complete stably rational classification of algebraic tori of dimensions and over a field . In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank and is given. The authors show that there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension , and there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension . The authors make a procedure to compute a flabby resolution of a -lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a -lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby -lattices of rank up to and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for -lattices holds when the rank , and fails when the rank is ...

Author : Igor Burban,Yuriy Drozd
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 51,9 Mb
Release : 2017-07-13
Category : Cohen-Macaulay modules
ISBN : 9781470425371

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Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems by Igor Burban,Yuriy Drozd Pdf

In this article the authors develop a new method to deal with maximal Cohen–Macaulay modules over non–isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen–Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen–Macaulay representation type. The authors' approach is illustrated on the case of k as well as several other rings. This study of maximal Cohen–Macaulay modules over non–isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.

Author : E. Delaygue,T. Rivoal,J. Roques
Publisher : American Mathematical Soc.
Page : 94 pages
File Size : 46,8 Mb
Release : 2017-02-20
Category : Congruences (Geometry)
ISBN : 9781470423001

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On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps by E. Delaygue,T. Rivoal,J. Roques Pdf

Using Dwork's theory, the authors prove a broad generalization of his famous -adic formal congruences theorem. This enables them to prove certain -adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the “Eisenstein constant” of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement “on average” of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases.