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Graph Theory
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. 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 th...
Modern Graph Theory
An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.
Graph Decompositions
Graph Decompositions is the first book on a topic that belongs mainly to infinite graph theory. It offers a complete account of the theory of simplicial decompositions of graphs, from its origins in the 1930s right up to present-day research.In addition to being one of the most important tools in infinite graph theory, simplicial decompositions may be seen as a model for any kind of structural graph decomposition. The currently topical tree-decompositions, for example, have their origin in simplicial decompositions.The text is centred around a few guiding problems and concepts, such as the existence and the uniqueness problem of simplicial decompositions into primes, or the concept of exclud...
Graph Theory
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Graphentheorie
Professionelle elektronische Ausgabe erhältlich direkt bei http://diestel-graph-theory.com/german/Profi.html Detailliert und klar, sowie stets mit Blick auf das Wesentliche, führt dieses Buch in die Graphentheorie ein. Zu jedem Themenkomplex stellt es sorgfältig die Grundlagen dar und beweist dann ein oder zwei tiefere typische Sätze, oftmals ergänzt durch eine informelle Diskussion ihrer tragenden Ideen. Es vermittelt so exemplarisch die wichtigsten Methoden der heutigen Graphentheorie, einschließlich moderner Techniken wie Regularitätslemma, Zufallsgraphen, Baumzerlegungen und Minoren. Aus den Besprechungen: "Eine hervorragende und mit größter Sorgfalt geschriebene Einführung in ...
Digraphs
The study of directed graphs (digraphs) has developed enormously over recent decades, yet the results are rather scattered across the journal literature. This is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, the authors discuss a large number of applications and their generalizations to topics such as the traveling salesman problem, project scheduling, genetics, network connectivity, and sparse matrices. Numerous exercises are included. For all graduate students, researchers and professionals interested in graph theory and its applications, this book will be essential reading.
Graph Theory
This standard textbook on modern graph theory 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 complete proofs, while offering glimpses of more advanced methods in each field via one or two deeper results. This is a major new edition. Among many other improvements, it offers additional tools for applying the regularity lemma, brings the tangle theory of graph minors up to the cutting edge of current research, and addresses new topics such as chi-boundedness in perfect graph theory. The book can be used as a reliable text for an introductory graduate course and is a...
Graph Coloring Problems
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.
Algebraic Combinatorics
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites inc...
Tangles
Discover how the theory of tangles identifies types of qualities in data sets, offering a structural approach to artificial intelligence.
