Extremal Graph Theory

This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.

Extremal Graph Theory

Author: Bela Bollobas

Publisher: Courier Corporation

ISBN: 0486317587

Page: 512

View: 979

The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory. Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. Although geared toward mathematicians and research students, much of Extremal Graph Theory is accessible even to undergraduate students of mathematics. Pure mathematicians will find this text a valuable resource in terms of its unusually large collection of results and proofs, and professionals in other fields with an interest in the applications of graph theory will also appreciate its precision and scope.

Extremal Graph Theory with Emphasis on Probabilistic Methods

In this book, an update of his 1978 book Extremal Graph Theory, the author focuses on a trend towards probabilistic methods.

Extremal Graph Theory with Emphasis on Probabilistic Methods

Author: Béla Bollobás

Publisher: American Mathematical Soc.

ISBN: 0821807129

Page: 64

View: 304

Problems in extremal graph theory have traditionally been tackled by ingenious methods which made use of the structure of extremal graphs. In this book, an update of his 1978 book ""Extremal Graph Theory"", the author focuses on a trend towards probabilistic methods. He demonstrates both the direct use of probability theory and, more importantly, the fruitful adoption of a probabilistic frame of mind when tackling main line extremal problems. Essentially self-contained, the book does not merely catalog results, but rather includes considerable discussion on a few of the deeper results. The author addresses pure mathematicians, especially combinatorialists and graduate students taking graph theory, as well as theoretical computer scientists. He assumes a mature familiarity with combinatorial methods and an acquaintance with basic graph theory. The book is based on the NSF-CBMS Regional Conference on Graph Theory held at Emory University in June, 1984.

Extremal Graph Theory with Emphasis on Probabilistic Methods

Extremal Graph Theory with Emphasis on Probabilistic Methods

Author: Béla Bollobás

Publisher: American Mathematical Soc.

ISBN: 0821807129

Page: 64

View: 862

Problems in extremal graph theory have traditionally been tackled by ingenious methods which made use of the structure of extremal graphs. In this book, an update of his 1978 book ""Extremal Graph Theory"", the author focuses on a trend towards probabilistic methods. He demonstrates both the direct use of probability theory and, more importantly, the fruitful adoption of a probabilistic frame of mind when tackling main line extremal problems. Essentially self-contained, the book does not merely catalog results, but rather includes considerable discussion on a few of the deeper results. The author addresses pure mathematicians, especially combinatorialists and graduate students taking graph theory, as well as theoretical computer scientists. He assumes a mature familiarity with combinatorial methods and an acquaintance with basic graph theory. The book is based on the NSF-CBMS Regional Conference on Graph Theory held at Emory University in June, 1984.

Extremal Graph Theory with Emphasis on Probabilistic Methods

In this book, an update of his 1978 book Extremal Graph Theory, the author focuses on a trend towards probabilistic methods.

Extremal Graph Theory with Emphasis on Probabilistic Methods

Author: Béla Bollobás

Publisher: American Mathematical Soc.

ISBN: 9780821889077

Page: 64

View: 999

Problems in extremal graph theory have traditionally been tackled by ingenious methods which made use of the structure of extremal graphs. In this book, an update of his 1978 book Extremal Graph Theory, the author focuses on a trend towards probabilistic methods. He demonstrates both the direct use of probability theory and, more importantly, the fruitful adoption of a probabilistic frame of mind when tackling main line extremal problems. Essentially self-contained, the book doesnot merely catalog results, but rather includes considerable discussion on a few of the deeper results. The author addresses pure mathematicians, especially combinatorialists and graduate students taking graph theory, as well as theoretical computer scientists. He assumes a mature familiarity withcombinatorial methods and an acquaintance with basic graph theory. The book is based on the NSF-CBMS Regional Conference on Graph Theory held at Emory University in June, 1984.

Modern Graph 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.

Modern Graph Theory

Author: Bela Bollobas

Publisher: Springer Science & Business Media

ISBN: 1461206197

Page: 394

View: 296

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.

Large Networks and Graph Limits

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.

Large Networks and Graph Limits

Author: László Lovász

Publisher: American Mathematical Soc.

ISBN: 0821890859

Page: 475

View: 853

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.

Graphs Matrices and Designs

This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.

Graphs  Matrices  and Designs

Author: Rees

Publisher: CRC Press

ISBN: 9780824787905

Page: 344

View: 904

Examines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.

Graph Theory

From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject.

Graph Theory

Author: Bela Bollobas

Publisher: Springer Science & Business Media

ISBN: 1461299675

Page: 180

View: 326

From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletin of the London Mathematical Society#1

Handbook of Graph Theory

The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published.

Handbook of Graph Theory

Author: Jonathan L. Gross

Publisher: CRC Press

ISBN: 9780203490204

Page: 1192

View: 770

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

Graph Theory

Finally, to the professional mathematician, the book affords an overview of graph theory as it stands today: with its typical questions and methods, its classic results, and some of those developments that have made it such an exciting area ...

Graph Theory

Author: Reinhard Diestel

Publisher: Springer Science & Business Media

ISBN: 9780387989761

Page: 312

View: 438

Almost two decades after the appearance of most of the classical texts on the theory, this fresh introduction offers a reassessment of the main fields, methods and results today. Viewed as a branch of pure mathematics, the theory of finite graphs is developed as a coherent subject in its own right, with its own unifying questions and methods. The book thus seeks to complement, not replace, the existing, more algorithmic treatments, and can be used at various levels. It contains all the standard material for a first undergraduate course, complete with detailed proofs and numerous illustrations. While, for graduates, the text offers proofs of several more advanced results, most of which appear in a book for the first time. These proofs are described with as much care and detail as their simpler counterparts, often with an informal discussion of their underlying ideas complementing their rigorous step-by-step account. Finally, to the professional mathematician, the book affords an overview of graph theory as it stands today: with its typical questions and methods, its classic results, and some of those developments that have made it such an exciting area in recent years.

Graph Theory

An introductory text in graph theory, this treatment covers primary techniques and includes both algorithmic and theoretical problems.

Graph Theory

Author: Ronald Gould

Publisher: Courier Corporation

ISBN: 0486320367

Page: 352

View: 651

An introductory text in graph theory, this treatment covers primary techniques and includes both algorithmic and theoretical problems. Algorithms are presented with a minimum of advanced data structures and programming details. 1988 edition.

Towards a Theory of Geometric Graphs

The present volume is a careful selection of 25 invited and thoroughly refereed papers, reporting about important recent discoveries on the way Towards a Theory of Geometric Graphs.

Towards a Theory of Geometric Graphs

Author: János Pach

Publisher: American Mathematical Soc.

ISBN: 0821834843

Page: 283

View: 730

The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical ""Theory of Finite and Infinite Graphs"", the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects.Many of the powerful techniques developed in these fields have been successfully applied in other areas of mathematics. However, the same methods were often incapable of providing satisfactory answers to questions arising in geometric applications. In the spirit of Konig, geometric graph theory focuses on combinatorial and geometric properties of graphs drawn in the plane by straight-line edges (or more generally, by edges represented by simple Jordan arcs). It is an emerging discipline that abounds in open problems, but it has already yielded some striking results which have proved instrumental in the solution of several basic problems in combinatorial and computational geometry. The present volume is a careful selection of 25 invited and thoroughly refereed papers, reporting about important recent discoveries on the way Towards a Theory of Geometric Graphs.

Introduction to Chemical Graph Theory

Preliminaries -- Distance in graphs and the Wiener index -- Vertex degrees and the Randic index -- Independent sets : Merrield-Simmons index and Hosoya index -- Graph spectra and the graph energy

Introduction to Chemical Graph Theory

Author: Stephan Wagner

Publisher: Chapman & Hall/CRC

ISBN: 9781138325081

Page: 259

View: 414

Preliminaries -- Distance in graphs and the Wiener index -- Vertex degrees and the Randic index -- Independent sets : Merrield-Simmons index and Hosoya index -- Graph spectra and the graph energy

Progress in Graph Theory

[18] P. Erdos and M. Simonovits: A limit theorem in graph theory, Studia Sci. Math
. Math. Hungary. l (1966) 51-57. [19] P. Erdos and M. Simonovits: Some extremal
problems in graph theory, Coll. Math. Soc. J. Bolyai 4 (1969) 377-390. [20] P.

Progress in Graph Theory

Author: Silver Jubilee Conference on Combinatorics (1982 : University of Waterloo)

Publisher: Toronto ; Orlando : Academic Press

ISBN:

Page: 539

View: 573

A Seminar on Graph Theory

Lectures given in F. Harary's seminar course, University College of London, Dept. of Mathematics, 1962-1963.

A Seminar on Graph Theory

Author: Frank Harary

Publisher: Courier Dover Publications

ISBN: 0486796841

Page: 128

View: 249

Lectures given in F. Harary's seminar course, University College of London, Dept. of Mathematics, 1962-1963.