Overview

Continuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and applications of graph theory. Nearly 50 percent longer than its bestselling predecessor, this edition reorganizes the material and presents many new topics. New to the Fifth Edition New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings New examples, figures, and applications to illustrate concepts and theorems Expanded historical discussions of well-known mathematicians and problems More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book Reorganization of sections into subsections to make the material easier to read Bolded definitions of terms, making them easier to locate Despite a field that has evolved over the years, this student-friendly, classroom-tested text remains the consummate introduction to graph theory. It explores the subject's fascinating history and presents a host of interesting problems and diverse applications.

Full Product Details

Author:   Gary Chartrand (Western Michigan University, Kalamazoo, USA) ,  Linda Lesniak (Western Michigan University, Kalamazoo, USA) ,  Ping Zhang (Western Michigan University, Kalamazoo, USA)
Publisher:   Taylor & Francis Inc
Imprint:   Taylor & Francis Inc
Edition:   5th New edition
Volume:   39
Dimensions:   Width: 15.60cm , Height: 3.60cm , Length: 23.40cm
Weight:   0.975kg
ISBN:  

9781439826270

ISBN 10:   1439826277
Pages:   598
Publication Date:   19 October 2010
Audience:   College/higher education ,  Undergraduate ,  Tertiary & Higher Education
Replaced By:   9781498735766
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   In Print  
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.

Table of Contents

Introduction to Graphs Graphs and Subgraphs Degree Sequences Connected Graphs and Distance Multigraphs and Digraphs Trees and Connectivity Nonseparable Graphs Trees Spanning Trees Connectivity and Edge-Connectivity Menger's Theorem Eulerian and Hamiltonian Graphs Eulerian Graphs Hamiltonian Graphs Powers of Graphs and Line Graphs Digraphs Strong Digraphs Tournaments Flows in Networks Graphs: History and Symmetry Some Historical Figures of Graph Theory The Automorphism Group of a Graph Cayley Color Graphs The Reconstruction Problem Planar Graphs The Euler Identity Planarity versus Nonplanarity The Crossing Number of a Graph Hamiltonian Planar Graphs Graph Embeddings The Genus of a Graph 2-Cell Embeddings of Graphs The Maximum Genus of a Graph The Graph Minor Theorem Vertex Colorings The Chromatic Number of a Graph Color-Critical Graphs Bounds for the Chromatic Number Perfect Graphs List Colorings Map Colorings The Four Color Problem Colorings of Planar Graphs The Conjectures of Hajos and Hadwiger Chromatic Polynomials The Heawood Map-Coloring Problem Matchings, Factorization, and Domination Matchings and Independence in Graphs Factorization Decomposition and Graceful Graphs Domination Edge Colorings Chromatic Index and Vizing's Theorem Class One and Class Two Graphs Tait Colorings Nowhere-Zero Flows List Edge Colorings and Total Colorings Extremal Graph Theory Turan's Theorem Cages Ramsey Theory Hints and Solutions to Odd-Numbered Exercises Bibliography Index of Names Index of Mathematical Terms List of Symbols

Reviews

Praise for the Fourth Edition ! a popular point of entry to the field ! has evolved with the field from a purely mathematical treatment to one that also addresses the needs of computer scientists. --L'Enseignement Mathematique ! emphasizes clear exposition, well-written proofs, and many original and innovative exercises of varying difficulty and challenge ! For 25 years, Graphs & Digraphs, in its various editions, has served as an exemplary introduction to the emerging mathematical disciplines of graph theories, for advanced undergraduate and graduate students. It has also served established graph theorists, combinatorialists, and other discrete mathematicians, as well as computer scientists and chemists, as a useful reference work. The fourth edition continues these fine traditions. --Zentralblatt MATH

As with the earlier editions, the current text emphasizes clear exposition, well-written proofs, and many original and innovative exercises of varying difficulty and challenge. ! The fifth edition continues and extends these fine traditions. --Arthur T. White, Zentralblatt MATH 1211 Now in its fifth edition, its success as a textbook is indicative of its quality and its clarity of presentation ! The authors also describe the fascinating history behind some of the key problems in graph theory, and, to a lesser extent, their applications. This book describes the key concepts you need to get started in graph theory ! . It provides all you might need to know about graph embeddings and graph colorings. Moreover, it analyzes many other topics that more general discrete mathematics monographs do not always cover, such as network flows, minimum cuts, matchings, factorization, decomposition, and even extremal graph theory ! this thorough textbook includes hundreds of exercises at the end of each section. Hints and solutions for odd-numbered exercises are included in the appendix, making it especially suitable for self-learning. --Fernando Berzal, Computing Reviews, September 2011 Praise for the Fourth Edition: ! a popular point of entry to the field ! has evolved with the field from a purely mathematical treatment to one that also addresses the needs of computer scientists. --L'Enseignement Mathematique ! emphasizes clear exposition, well-written proofs, and many original and innovative exercises of varying difficulty and challenge ! For 25 years, Graphs & Digraphs, in its various editions, has served as an exemplary introduction to the emerging mathematical disciplines of graph theories, for advanced undergraduate and graduate students. It has also served established graph theorists, combinatorialists, and other discrete mathematicians, as well as computer scientists and chemists, as a useful reference work. The fourth edition continues these fine traditions. --Zentralblatt MATH

Author Information

Gary Chartrand is a professor emeritus of mathematics at Western Michigan University. Linda Lesniak is a professor emeritus of mathematics at Drew University. Ping Zhang is a professor of mathematics at Western Michigan University. All three have authored or co-authored many textbooks in mathematics and numerous research articles in graph theory.

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