Graphs & Digraphs
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Graphs & Digraphs

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Description

Graphs & Digraphs masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory.


Fully updated and thoughtfully reorganized to make reading and locating material easier for instructors and students, the Sixth Edition of this bestselling, classroom-tested text:




Adds more than 160 new exercises
Presents many new concepts, theorems, and examples
Includes recent major contributions to long-standing conjectures such as the Hamiltonian Factorization Conjecture, 1-Factorization Conjecture, and Alspach's Conjecture on graph decompositions
Supplies a proof of the perfect graph theorem
Features a revised chapter on the probabilistic method in graph theory with many results integrated throughout the text


At the end of the book are indices and lists of mathematicians' names, terms, symbols, and useful references. There is also a section giving hints and solutions to all odd-numbered exercises. A complete solutions manual is available with qualifying course adoption.


Graphs & Digraphs, Sixth Edition remains the consummate text for an advanced undergraduate level or introductory graduate level course or two-semester sequence on graph theory, exploring the subject's fascinating history while covering a host of interesting problems and diverse applications.
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Product details

  • Hardback | 640 pages
  • 156 x 235 x 38.1mm | 1,036g
  • Productivity Press
  • Portland, United States
  • English
  • New edition
  • 6th New edition
  • 343 Illustrations, black and white
  • 1498735762
  • 9781498735766
  • 642,675

Table of contents

Introduction
Graphs
The Degree of a Vertex
Isomorphic Graphs
Regular Graphs
Bipartite Graphs
Operations on Graphs
Degree Sequences
Multigraphs
Exercises for Chapter 1


Connected Graphs and Distance
Connected Graphs
Distance in Graphs
Exercises for Chapter 2


Trees
Nonseparable Graphs
Introduction to Trees
Spanning Trees
The Minimum Spanning Tree Problem
Exercises for Chapter 3


Connectivity
Connectivity and Edge-Connectivity
Theorems of Menger and Whitney
Exercises for Chapter 4


Eulerian Graphs
The Koenigsberg Bridge Problem
Eulerian Circuits and Trails
Exercises for Chapter 5


Hamiltonian Graphs
Hamilton's Icosian Game
Sufficient Conditions for Hamiltonicity
Toughness of Graphs
Highly Hamiltonian Graphs
Powers of Graphs and Line Graphs
Exercises for Chapter 6


Digraphs
Introduction to Digraphs
Strong Digraphs
Eulerian and Hamiltonian Digraphs
Tournaments
Kings in Tournaments
Hamiltonian Tournaments
Exercises for Chapter 7


Flows in Networks
Networks
The Max-Flow Min-Cut Theorem
Menger Theorems for Digraphs
Exercises for Chapter 8


Automorphisms and Reconstruction
The Automorphism Group of a Graph
Cayley Color Graphs
The Reconstruction Problem
Exercises for Chapter 9


Planar Graphs
The Euler Identity
Maximal Planar Graphs
Characterizations of Planar Graphs
Hamiltonian Planar Graphs
Exercises for Chapter 10


Nonplanar Graphs
The Crossing Number of a Graph
The Genus of a Graph
The Graph Minor Theorem
Exercises for Chapter 11


Matchings, Independence and Domination
Matchings
1-Factors
Independence and Covers
Domination
Exercises for Chapter 12


Factorization and Decomposition
Factorization
Decomposition
Cycle Decomposition
Graceful Graphs
Exercises for Chapter 13


Vertex Colorings
The Chromatic Number of a Graph
Color-Critical Graphs
Bounds for the Chromatic Number
Exercises for Chapter 14


Perfect Graphs and List Colorings
Perfect Graphs
The Perfect and Strong Perfect Graph Theorems
List Colorings
Exercises for Chapter 15


Map Colorings
The Four Color Problem
Colorings of Planar Graphs
List Colorings of Planar Graphs
The Conjectures of Hajos and Hadwiger
Chromatic Polynomials
The Heawood Map-Coloring Problem
Exercises for Chapter 16


Edge Colorings
The Chromatic Index of a Graph
Class One and Class Two Graphs
Tait Colorings
Exercises for Chapter 17


Nowhere-Zero Flows, List Edge Colorings
Nowhere-Zero Flows
List Edge Colorings
Total Colorings
Exercises for Chapter 18


Extremal Graph Theory
Turan's Theorem
Extremal Subgraphs
Cages
Exercises for Chapter 19


Ramsey Theory
Classical Ramsey Numbers
More General Ramsey Numbers
Exercises for Chapter 20


The Probabilistic Method
The Probabilistic Method
Random Graphs
Exercises for Chapter 21


Hints and Solutions to Odd-Numbered Exercises


Bibliography


Supplemental References


Index of Names


Index of Mathematical Terms


List of Symbols
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Review quote

Praise for the Previous Edition


"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


"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
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About Gary Chartrand

Gary Chartrand is a professor emeritus of mathematics at Western Michigan University, Kalamazoo, Michigan, USA. Linda Lesniak, a professor emeritus of mathematics from Drew University, Madison, New Jersey, USA, is currently a visiting mathematician at Western Michigan University, Kalamazoo, Michigan, USA. Ping Zhang is a professor of mathematics at Western Michigan University, Kalamazoo, Michigan, USA. All three have authored or coauthored many textbooks in mathematics and numerous research articles in graph theory.
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Rating details

15 ratings
4.06 out of 5 stars
5 53% (8)
4 27% (4)
3 0% (0)
2 13% (2)
1 7% (1)
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