Modern Graph Theory


Author: Bela Bollobas

Publisher: Springer Science & Business Media

ISBN: 1461206197

Category: Mathematics

Page: 394

View: 2377

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 Theory

Springer Graduate Text GTM 173


Author: Reinhard Diestel

Publisher: Reinhard Diestel



Page: 451

View: 7160

This standard textbook of modern graph theory, now in its fourth 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. Various eBook editions for computers and tablets are available from the author's website for the book, at a 72% discount. 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 “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 "Deep, clear, wonderful" Ron Graham in SIAM book reviews “…like listening to someone explain mathematics.” Bulletin of the AMS

A First Course in Graph Theory and Combinatorics


Author: Sebastian M. Cioabă

Publisher: Springer

ISBN: 9386279398

Category: Mathematics

Page: 186

View: 4582

The concept of a graph is fundamental in mathematics since it conveniently encodes diverse relations and facilitates combinatorial analysis of many complicated counting problems. In this book, the authors have traced the origins of graph theory from its humble beginnings of recreational mathematics to its modern setting for modeling communication networks as is evidenced by the World Wide Web graph used by many Internet search engines. This book is an introduction to graph theory and combinatorial analysis. It is based on courses given by the second author at Queen's University at Kingston, Ontario, Canada between 2002 and 2008. The courses were aimed at students in their final year of their undergraduate program.

Graph Theory for Operations Research and Management: Applications in Industrial Engineering

Applications in Industrial Engineering


Author: Farahani, Reza Zanjirani

Publisher: IGI Global

ISBN: 1466626925

Category: Technology & Engineering

Page: 367

View: 3805

While typically many approaches have been mainly mathematics focused, graph theory has become a tool used by scientists, researchers, and engineers in using modeling techniques to solve real-world problems. Graph Theory for Operations Research and Management: Applications in Industrial Engineering presents traditional and contemporary applications of graph theory in the areas of industrial engineering, management science, and applied operations research. This comprehensive collection of research introduces the useful basic concepts of graph theory in real world applications.

Anschauliche Funktionentheorie


Author: Tristan Needham

Publisher: Oldenbourg Wissenschaftsverlag

ISBN: 9783486709025

Category: Mathematics

Page: 685

View: 2520

Needhams neuartiger Zugang zur Funktionentheorie wurde von der Fachpresse begeistert aufgenommen. Mit über 500 zum großen Teil perspektivischen Grafiken vermittelt er im wahrsten Sinne des Wortes eine Anschauung von der sonst oft als trocken empfundenen Funktionentheorie. 'Anschauliche Funktionentheorie ist eine wahre Freude und ein Buch so recht nach meinem Herzen. Indem er ausschließlich seine neuartige geometrische Perspektive verwendet, enthüllt Tristan Needham viele überraschende und bisher weitgehend unbeachtete Facetten der Schönheit der Funktionentheorie.' (Sir Roger Penrose)

Kombinatorische Optimierung

Theorie und Algorithmen


Author: Bernhard Korte,Jens Vygen

Publisher: Springer-Verlag

ISBN: 3540769196

Category: Mathematics

Page: 675

View: 5071

Das Lehrbuch ist die deutsche Übersetzung der 4., wesentlich erweiterten Auflage des Titels „Combinatorial Optimization – Theory and Algorithms". Es gibt den neuesten Stand der kombinatorischen Optimierung wieder und liefert vornehmlich theoretische Resultate und Algorithmen mit beweisbar guten Laufzeiten und Ergebnissen, jedoch keine Heuristiken. Enthalten sind vollständige Beweise, auch für viele tiefe und neue Resultate, von denen einige bisher in der Lehrbuchliteratur noch nicht erschienen sind. Mit Übungen und umfassendem Literaturverzeichnis.

Adventures in Graph Theory


Author: W. David Joyner,Caroline Grant Melles

Publisher: Birkhäuser

ISBN: 3319683837

Category: Mathematics

Page: 327

View: 3762

This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.

Trigonometrie für Dummies


Author: Mary Jane Sterling

Publisher: John Wiley & Sons

ISBN: 3527638563

Category: Mathematics

Page: 377

View: 3665

Trigonometrie besch?ftigt sich mit Winkeln und Dreiecken. Das h?rt sich ja ganz einfach an, aber jeder, der sich schon mit Trigonometrie besch?ftigen durfte, wei? wie verdammt kniffelig sie sein kann. ?Trigonometrie f?r Dummies? f?hrt die Leser in diese sonderbare Welt ein und versucht dabei auch zu zeigen wo, wann und warum es sinnvoll ist, sich mit diesem Thema zu besch?ftigen. Am Ende sind dann Sinus, Cosinus, Tangens und Cotangens keine Fremden mehr sondern gute alte Bekannte.

A Textbook of Graph Theory


Author: R. Balakrishnan,K. Ranganathan

Publisher: Springer Science & Business Media

ISBN: 1461445280

Category: Mathematics

Page: 292

View: 6540

In its second edition, expanded with new chapters on domination in graphs and on the spectral properties of graphs, this book offers a solid background in the basics of graph theory. Introduces such topics as Dirac's theorem on k-connected graphs and more.

Graphs on Surfaces

Dualities, Polynomials, and Knots


Author: Joanna A. Ellis-Monaghan,Iain Moffatt

Publisher: Springer Science & Business Media

ISBN: 1461469716

Category: Mathematics

Page: 139

View: 703

Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.

Das BUCH der Beweise


Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3662064545

Category: Mathematics

Page: 247

View: 9894

Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit

A Beginner's Guide to Graph Theory


Author: W.D. Wallis

Publisher: Springer Science & Business Media

ISBN: 9780817645809

Category: Mathematics

Page: 260

View: 2929

Concisely written, gentle introduction to graph theory suitable as a textbook or for self-study Graph-theoretic applications from diverse fields (computer science, engineering, chemistry, management science) 2nd ed. includes new chapters on labeling and communications networks and small worlds, as well as expanded beginner's material Many additional changes, improvements, and corrections resulting from classroom use



Author: Reinhard Diestel

Publisher: Springer Science & Business Media

ISBN: 9783540213918

Category: Graph theory

Page: 344

View: 2278

Die nunmehr dritte Auflage des von der Kritik hochgelobten Springer Graduate Texts, Graph Theory, erscheint hier in einer dem englischen Original weitgehend angeglichenen und nur leicht gekurzten deutschen Fassung: als verlassliche Textgrundlage fur deutschsprachige Vorlesungen (auch einfuhrende), sowie zum Selbststudium. Aus der Kritik der englischen Originalausgabe (GTM 173): "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 "This book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory." Bulletin of the ICA ..".like listening to someone explain mathematics." Bulletin of the AMS Weitere Informationen, und Online-Ausgabe zum Testen:

Algebraic Graph Theory


Author: Chris Godsil,Gordon F. Royle

Publisher: Springer

ISBN: 9780387952413

Category: Mathematics

Page: 439

View: 2922

Algebraic graph theory is a fascinating subject concerned with the interplay between algebra and graph theory. Algebraic tools can be used to give surprising and elegant proofs of graph theoretic facts, and there are many interesting algebraic objects associated with graphs. The authors take an inclusive view of the subject, and present a wide range of topics. These range from standard classics, such as the characterization of line graphs by eigenvalues, to more unusual areas such as geometric embeddings of graphs and the study of graph homomorphisms. The authors' goal has been to present each topic in a self-contained fashion, presenting the main tools and ideas, with an emphasis on their use in understanding concrete examples. A substantial proportion of the book covers topics that have not appeared in book form before, and as such it provides an accessible introduction to the research literature and to important open questions in modern algebraic graph theory. This book is primarily aimed at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general. However, all the necessary graph theory is developed from scratch, so the only pre-requisite for reading it is a first course in linear algebra and a small amount of elementary group theory. It should be accessible to motivated upper-level undergraduates. Chris Godsil is a full professor in the Department of Combinatorics and Optimization at the University of Waterloo. His main research interests lie in the interactions between algebra and combinatorics, in particular the application of algebraic techniques to graphs, designs and codes. He has published more than 70 papers in these areas, is a founding editor of "The Journal of Algebraic Combinatorics" and is the author of the book "Algebraic Combinatorics". Gordon Royle teaches in the Department of Computer Science & Software Engineering at the University of Western Australia. His main research interests lie in the application of computers to combinatorial problems, in particular the cataloguing, enumeration and investigation of graphs, designs and finite geometries. He has published more than30 papers in graph theory, design theory and finite geometry.

Algebra und Diskrete Mathematik 2

Lineare Optimierung, Graphen und Algorithmen, Algebraische Strukturen und Allgemeine Algebra mit Anwendungen


Author: Dietlinde Lau

Publisher: Springer-Verlag

ISBN: 354035025X

Category: Mathematics

Page: 494

View: 3375

Algebra und Diskrete Mathematik gehören zu den wichtigsten Grundlagen der Informatik. Ein umfassendes und leicht verständliches Lehrbuch in 2 Bänden: klar herausgearbeitete Lösungsalgorithmen, viele Beispiele, ausführliche Beweise, Hervorhebungen wichtiger Inhalte. Plus: umfangreiche Sammlung von Übungen und Anwendungsmöglichkeiten. In Band 2: Lineare Optimierung, Graphen/Algorithmen, Algebraische Strukturen, Allgemeine Algebra mit Anwendungen.

Algorithmen in C


Author: Robert Sedgewick

Publisher: Pearson Deutschland GmbH

ISBN: 9783893193769

Category: Algorithmus

Page: 742

View: 765

Vorlesungen über die Theorie der algebraischen Zahlen


Author: Erich Hecke

Publisher: University of Pennsylvania Press

ISBN: 9780821821435

Category: Mathematics

Page: 274

View: 8339

This title has been described as An elegant and comprehensive account of the modern theory of algebraic numbers - Bulletin of the AMS.

Differentialgleichungen und ihre Anwendungen


Author: Martin Braun

Publisher: Springer-Verlag

ISBN: 3642973418

Category: Mathematics

Page: 596

View: 5275

Dieses richtungsweisende Lehrbuch für die Anwendung der Mathematik in anderen Wissenschaftszweigen gibt eine Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Fortran und APL-Programme geben den Studenten die Möglichkeit, verschiedene numerische Näherungsverfahren an ihrem PC selbst durchzurechnen. Aus den Besprechungen: "Die Darstellung ist überall mathematisch streng und zudem ungemein anregend. Abgesehen von manchen historischen Bemerkungen ... tragen dazu die vielen mit ausführlichem Hintergrund sehr eingehend entwickelten praktischen Anwendungen bei. ... Besondere Aufmerksamkeit wird der physikalisch und technisch so wichtigen Frage nach Stabilität von Lösungen eines Systems von Differentialgleichungen gewidmet. Das Buch ist wegen seiner geringen Voraussetzungen und vorzüglichen Didaktik schon für alle Studenten des 3. Semesters geeignet; seine eminent praktische Haltung empfiehlt es aber auch für alle Physiker, die mit Differentialgleichungen und ihren Anwendungen umzugehen haben." #Physikalische Blätter#