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Some Topics In Graph Homomorphisms
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Book Synopsis Graphs and Homomorphisms by : Pavol Hell
Download or read book Graphs and Homomorphisms written by Pavol Hell and published by OUP Oxford. This book was released on 2004-07-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics. Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level and has been used for courses at Simon Fraser University (Vancouver), Charles University (Prague), ETH (Zurich), and UFRJ (Rio de Janeiro). The exercises vary in difficulty. The first few are usually intended to give the reader an opportunity to practice the concepts introduced in the chapter; the later ones explore related concepts, or even introduce new ones. For the harder exercises hints and references are provided. The authors are well known for their research in this area and the book will be invaluable to graduate students and researchers alike.
Book Synopsis Topics in Graph Theory by : Jonathan L Gross
Download or read book Topics in Graph Theory written by Jonathan L Gross and published by CRC Press. This book was released on 2023-05-24 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay continues to grow between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences. Topics in Graph Theory is geared toward the more mathematically mature student. The first three chapters provide the basic definitions and theorems of graph theory and the remaining chapters introduce a variety of topics and directions for research. These topics draw on numerous areas of theoretical and applied mathematics, including combinatorics, probability, linear algebra, group theory, topology, operations research, and computer science. This makes the book appropriate for a first course at the graduate level or as a second course at the undergraduate level. The authors build upon material previously published in Graph Theory and Its Applications, Third Edition, by the same authors. That text covers material for both an undergraduate and graduate course, while this book builds on and expands the graduate-level material. Features Extensive exercises and applications. Flexibility: appropriate for either a first course at the graduate level or an advanced course at the undergraduate level. Opens avenues to a variety of research areas in graph theory. Emphasis on topological and algebraic graph theory.
Book Synopsis Topics in Algorithmic Graph Theory by : Lowell W. Beineke
Download or read book Topics in Algorithmic Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2021-06-03 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic graph theory has been expanding at an extremely rapid rate since the middle of the twentieth century, in parallel with the growth of computer science and the accompanying utilization of computers, where efficient algorithms have been a prime goal. This book presents material on developments on graph algorithms and related concepts that will be of value to both mathematicians and computer scientists, at a level suitable for graduate students, researchers and instructors. The fifteen expository chapters, written by acknowledged international experts on their subjects, focus on the application of algorithms to solve particular problems. All chapters were carefully edited to enhance readability and standardize the chapter structure as well as the terminology and notation. The editors provide basic background material in graph theory, and a chapter written by the book's Academic Consultant, Martin Charles Golumbic (University of Haifa, Israel), provides background material on algorithms as connected with graph theory.
Book Synopsis Topics in Discrete Mathematics by : Martin Klazar
Download or read book Topics in Discrete Mathematics written by Martin Klazar and published by Springer Science & Business Media. This book was released on 2007-05-28 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jarik Nešetril. Leading experts have contributed survey and research papers in the areas of Algebraic Combinatorics, Combinatorial Number Theory, Game theory, Ramsey Theory, Graphs and Hypergraphs, Homomorphisms, Graph Colorings and Graph Embeddings.
Book Synopsis Topics in Chromatic Graph Theory by : Lowell W. Beineke
Download or read book Topics in Chromatic Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2015-05-07 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chromatic graph theory is a thriving area that uses various ideas of 'colouring' (of vertices, edges, and so on) to explore aspects of graph theory. It has links with other areas of mathematics, including topology, algebra and geometry, and is increasingly used in such areas as computer networks, where colouring algorithms form an important feature. While other books cover portions of the material, no other title has such a wide scope as this one, in which acknowledged international experts in the field provide a broad survey of the subject. All fifteen chapters have been carefully edited, with uniform notation and terminology applied throughout. Bjarne Toft (Odense, Denmark), widely recognized for his substantial contributions to the area, acted as academic consultant. The book serves as a valuable reference for researchers and graduate students in graph theory and combinatorics and as a useful introduction to the topic for mathematicians in related fields.
Book Synopsis Topics in Algebraic Graph Theory by : Lowell W. Beineke
Download or read book Topics in Algebraic Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2004-10-04 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no other book with such a wide scope of both areas of algebraic graph theory.
Book Synopsis Large Networks and Graph Limits by : László Lovász
Download or read book Large Networks and Graph Limits written by László Lovász and published by American Mathematical Soc.. This book was released on 2012 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks. To develop a mathematical theory of very large networks is an important challenge. This book describes one recent approach to this theory, the limit theory of graphs, which has emerged over the last decade. The theory has rich connections with other approaches to the study of large networks, such as ``property testing'' in computer science and regularity partition in graph theory. It has several applications in extremal graph theory, including the exact formulations and partial answers to very general questions, such as which problems in extremal graph theory are decidable. It also has less obvious connections with other parts of mathematics (classical and non-classical, like probability theory, measure theory, tensor algebras, and semidefinite optimization). This book explains many of these connections, first at an informal level to emphasize the need to apply more advanced mathematical methods, and then gives an exact development of the theory of the algebraic theory of graph homomorphisms and of the analytic theory of graph limits. This is an amazing book: readable, deep, and lively. It sets out this emerging area, makes connections between old classical graph theory and graph limits, and charts the course of the future. --Persi Diaconis, Stanford University This book is a comprehensive study of the active topic of graph limits and an updated account of its present status. It is a beautiful volume written by an outstanding mathematician who is also a great expositor. --Noga Alon, Tel Aviv University, Israel Modern combinatorics is by no means an isolated subject in mathematics, but has many rich and interesting connections to almost every area of mathematics and computer science. The research presented in Lovasz's book exemplifies this phenomenon. This book presents a wonderful opportunity for a student in combinatorics to explore other fields of mathematics, or conversely for experts in other areas of mathematics to become acquainted with some aspects of graph theory. --Terence Tao, University of California, Los Angeles, CA Laszlo Lovasz has written an admirable treatise on the exciting new theory of graph limits and graph homomorphisms, an area of great importance in the study of large networks. It is an authoritative, masterful text that reflects Lovasz's position as the main architect of this rapidly developing theory. The book is a must for combinatorialists, network theorists, and theoretical computer scientists alike. --Bela Bollobas, Cambridge University, UK
Book Synopsis Graph Coloring Problems by : Tommy R. Jensen
Download or read book Graph Coloring Problems written by Tommy R. Jensen and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys.
Book Synopsis Handbook of the Tutte Polynomial and Related Topics by : Joanna A. Ellis-Monaghan
Download or read book Handbook of the Tutte Polynomial and Related Topics written by Joanna A. Ellis-Monaghan and published by CRC Press. This book was released on 2022-07-06 with total page 805 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied graph polynomials. Handbook of the Tutte Polynomial and Related Topics is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters written by experts in the field, which collectively offer a concise overview of the polynomial’s many properties and applications. Each chapter covers a different aspect of the Tutte polynomial and contains the central results and references for its topic. The chapters are organized into six parts. Part I describes the fundamental properties of the Tutte polynomial, providing an overview of the Tutte polynomial and the necessary background for the rest of the handbook. Part II is concerned with questions of computation, complexity, and approximation for the Tutte polynomial; Part III covers a selection of related graph polynomials; Part IV discusses a range of applications of the Tutte polynomial to mathematics, physics, and biology; Part V includes various extensions and generalizations of the Tutte polynomial; and Part VI provides a history of the development of the Tutte polynomial. Features Written in an accessible style for non-experts, yet extensive enough for experts Serves as a comprehensive and accessible introduction to the theory of graph polynomials for researchers in mathematics, physics, and computer science Provides an extensive reference volume for the evaluations, theorems, and properties of the Tutte polynomial and related graph, matroid, and knot invariants Offers broad coverage, touching on the wide range of applications of the Tutte polynomial and its various specializations
Download or read book Graph Symmetry written by Gena Hahn and published by Springer Science & Business Media. This book was released on 1997-06-30 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.
Book Synopsis Algebraic Graph Theory by : Chris Godsil
Download or read book Algebraic Graph Theory written by Chris Godsil and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.
Book Synopsis Handbook of Graph Theory, Second Edition by : Jonathan L. Gross
Download or read book Handbook of Graph Theory, Second Edition written by Jonathan L. Gross and published by CRC Press. This book was released on 2013-12-17 with total page 1634 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition—over 400 pages longer than its predecessor—incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.
Book Synopsis Category Theory for the Sciences by : David I. Spivak
Download or read book Category Theory for the Sciences written by David I. Spivak and published by MIT Press. This book was released on 2014-10-17 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
Book Synopsis From Domination to Coloring by : Gary Chartrand
Download or read book From Domination to Coloring written by Gary Chartrand and published by Springer Nature. This book was released on 2019-10-16 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is in honor of the 80th birthday of Stephen Hedetniemi. It describes advanced material in graph theory in the areas of domination, coloring, spanning cycles and circuits, and distance that grew out of research topics investigated by Stephen Hedetniemi. The purpose of this book is to provide background and principal results on these topics, along with same related problems and conjectures, for researchers in these areas. The most important features deal with material, results, and problems that researchers may not be aware of but may find of interest. Each chapter contains results, methods and information that will give readers the necessary background to investigate each topic in more detail.
Book Synopsis Handbook of Graph Theory by : Jonathan L. Gross
Download or read book Handbook of Graph Theory written by Jonathan L. Gross and published by CRC Press. This book was released on 2003-12-29 with total page 1200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approach
Book Synopsis Chromatic Graph Theory by : Gary Chartrand
Download or read book Chromatic Graph Theory written by Gary Chartrand and published by CRC Press. This book was released on 2019-11-28 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition
Book Synopsis Large Deviations for Random Graphs by : Sourav Chatterjee
Download or read book Large Deviations for Random Graphs written by Sourav Chatterjee and published by Springer. This book was released on 2017-08-31 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics.
