Proof Of The 1 Factorization And Hamilton Decomposition Conjectures

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Proof of the 1-Factorization and Hamilton Decomposition Conjectures

Author : Béla Csaba
Publisher : American Mathematical Soc.
ISBN 13 : 1470420252
Total Pages : 176 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Proof of the 1-Factorization and Hamilton Decomposition Conjectures by : Béla Csaba

Download or read book Proof of the 1-Factorization and Hamilton Decomposition Conjectures written by Béla Csaba and published by American Mathematical Soc.. This book was released on 2016-10-05 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Proof of the 1-Factorization and Hamilton Decomposition Conjectures

Author :
Publisher :
ISBN 13 : 9781470435080
Total Pages : pages
Book Rating : 4.4/5 (35 download)

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Book Synopsis Proof of the 1-Factorization and Hamilton Decomposition Conjectures by :

Download or read book Proof of the 1-Factorization and Hamilton Decomposition Conjectures written by and published by . This book was released on 2016-10-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Seventh European Conference on Combinatorics, Graph Theory and Applications

Author : Jaroslav Nešetřil
Publisher : Springer Science & Business Media
ISBN 13 : 887642475X
Total Pages : 612 pages
Book Rating : 4.8/5 (764 download)

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Book Synopsis The Seventh European Conference on Combinatorics, Graph Theory and Applications by : Jaroslav Nešetřil

Download or read book The Seventh European Conference on Combinatorics, Graph Theory and Applications written by Jaroslav Nešetřil and published by Springer Science & Business Media. This book was released on 2014-01-18 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Extended Abstracts EuroComb 2021

Author : Jaroslav Nešetřil
Publisher : Springer Nature
ISBN 13 : 3030838234
Total Pages : 875 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Extended Abstracts EuroComb 2021 by : Jaroslav Nešetřil

Download or read book Extended Abstracts EuroComb 2021 written by Jaroslav Nešetřil and published by Springer Nature. This book was released on 2021-08-23 with total page 875 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Graphs & Digraphs

Author : Gary Chartrand
Publisher : CRC Press
ISBN 13 : 1003801080
Total Pages : 365 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Graphs & Digraphs by : Gary Chartrand

Download or read book Graphs & Digraphs written by Gary Chartrand and published by CRC Press. This book was released on 2024-01-23 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Graph Theory

Author : Ralucca Gera
Publisher : Springer
ISBN 13 : 3319976869
Total Pages : 281 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Graph Theory by : Ralucca Gera

Download or read book Graph Theory written by Ralucca Gera and published by Springer. This book was released on 2018-10-26 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Graph Theory

Author : Karin R Saoub
Publisher : CRC Press
ISBN 13 : 0429779879
Total Pages : 394 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Graph Theory by : Karin R Saoub

Download or read book Graph Theory written by Karin R Saoub and published by CRC Press. This book was released on 2021-03-17 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Needle Decompositions in Riemannian Geometry

Author : Bo’az Klartag
Publisher : American Mathematical Soc.
ISBN 13 : 1470425424
Total Pages : 90 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Needle Decompositions in Riemannian Geometry by : Bo’az Klartag

Download or read book Needle Decompositions in Riemannian Geometry written by Bo’az Klartag and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fundamentals of Graph Theory

Author : Allan Bickle
Publisher : American Mathematical Soc.
ISBN 13 : 1470453428
Total Pages : 336 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Fundamentals of Graph Theory by : Allan Bickle

Download or read book Fundamentals of Graph Theory written by Allan Bickle and published by American Mathematical Soc.. This book was released on 2020-03-10 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topologically Protected States in One-Dimensional Systems

Author : Charles Fefferman
Publisher : American Mathematical Soc.
ISBN 13 : 1470423235
Total Pages : 132 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topologically Protected States in One-Dimensional Systems by : Charles Fefferman

Download or read book Topologically Protected States in One-Dimensional Systems written by Charles Fefferman and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Surveys in Combinatorics 2017

Author : Anders Claesson
Publisher : Cambridge University Press
ISBN 13 : 1108350356
Total Pages : 451 pages
Book Rating : 4.1/5 (83 download)

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Book Synopsis Surveys in Combinatorics 2017 by : Anders Claesson

Download or read book Surveys in Combinatorics 2017 written by Anders Claesson and published by Cambridge University Press. This book was released on 2017-06-30 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains nine survey articles which provide expanded accounts of plenary seminars given at the British Combinatorial Conference at the University of Strathclyde in July 2017. This biennial conference is a well-established international event attracting speakers from around the world. Written by internationally recognised experts in the field, these articles represent a timely snapshot of the state of the art in the different areas of combinatorics. Topics covered include the robustness of graph properties, the spt-function of Andrews, switching techniques for edge decompositions of graphs, monotone cellular automata, and applications of relative entropy in additive combinatorics. The book will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.

Intersection Local Times, Loop Soups and Permanental Wick Powers

Author : Yves Le Jan
Publisher : American Mathematical Soc.
ISBN 13 : 1470436957
Total Pages : 92 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Intersection Local Times, Loop Soups and Permanental Wick Powers by : Yves Le Jan

Download or read book Intersection Local Times, Loop Soups and Permanental Wick Powers written by Yves Le Jan and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several stochastic processes related to transient Lévy processes with potential densities , that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures endowed with a metric . Sufficient conditions are obtained for the continuity of these processes on . The processes include -fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup -fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of -th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above.

On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps

Author : E. Delaygue
Publisher : American Mathematical Soc.
ISBN 13 : 1470423006
Total Pages : 106 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps by : E. Delaygue

Download or read book On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps written by E. Delaygue and published by American Mathematical Soc.. This book was released on 2017-02-20 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Oseledec Multiplicative Ergodic Theorem for Laminations

Author : Viêt-Anh Nguyên
Publisher : American Mathematical Soc.
ISBN 13 : 1470422530
Total Pages : 190 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Oseledec Multiplicative Ergodic Theorem for Laminations by : Viêt-Anh Nguyên

Download or read book Oseledec Multiplicative Ergodic Theorem for Laminations written by Viêt-Anh Nguyên and published by American Mathematical Soc.. This book was released on 2017-02-20 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a -dimensional lamination endowed with a Riemannian metric, the author introduces the notion of a multiplicative cocycle of rank , where and are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, the author defines the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. He also proves an Oseledec multiplicative ergodic theorem in this context. This theorem implies the existence of an Oseledec decomposition almost everywhere which is holonomy invariant. Moreover, in the case of differentiable cocycles the author establishes effective integral estimates for the Lyapunov exponents. These results find applications in the geometric and dynamical theory of laminations. They are also applicable to (not necessarily closed) laminations with singularities. Interesting holonomy properties of a generic leaf of a foliation are obtained. The main ingredients of the author's method are the theory of Brownian motion, the analysis of the heat diffusions on Riemannian manifolds, the ergodic theory in discrete dynamics and a geometric study of laminations.

Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory

Author : H. Hofer
Publisher : American Mathematical Soc.
ISBN 13 : 1470422034
Total Pages : 230 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory by : H. Hofer

Download or read book Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory written by H. Hofer and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyfold theory the authors use the results of the present paper to describe an alternative construction of the Gromov-Witten invariants for general compact symplectic manifolds.

Rationality Problem for Algebraic Tori

Author : Akinari Hoshi
Publisher : American Mathematical Soc.
ISBN 13 : 1470424096
Total Pages : 228 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Rationality Problem for Algebraic Tori by : Akinari Hoshi

Download or read book Rationality Problem for Algebraic Tori written by Akinari Hoshi and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ...

Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems

Author : Igor Burban
Publisher : American Mathematical Soc.
ISBN 13 : 1470425378
Total Pages : 134 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems by : Igor Burban

Download or read book Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems written by Igor Burban and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.