Graphs Theory and Applications: With Exercises and Problems [NOOK Book]

Overview

This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus ...
See more details below
Graphs Theory and Applications: With Exercises and Problems

Available on NOOK devices and apps  
  • NOOK Devices
  • Samsung Galaxy Tab 4 NOOK 7.0
  • Samsung Galaxy Tab 4 NOOK 10.1
  • NOOK HD Tablet
  • NOOK HD+ Tablet
  • NOOK eReaders
  • NOOK Color
  • NOOK Tablet
  • Tablet/Phone
  • NOOK for Windows 8 Tablet
  • NOOK for iOS
  • NOOK for Android
  • NOOK Kids for iPad
  • PC/Mac
  • NOOK for Windows 8
  • NOOK for PC
  • NOOK for Mac
  • NOOK for Web

Want a NOOK? Explore Now

NOOK Book (eBook)
$79.99
BN.com price
(Save 42%)$140.00 List Price
Note: This NOOK Book can be purchased in bulk. Please email us for more information.

Overview

This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the subject. An appendix outlines the basis of computational complexity theory, in particular the definition of NP-completeness, which is essential for algorithmic applications.
Read More Show Less

Product Details

  • ISBN-13: 9781118623091
  • Publisher: Wiley
  • Publication date: 5/6/2013
  • Series: ISTE
  • Sold by: Barnes & Noble
  • Format: eBook
  • Edition number: 1
  • File size: 3 MB

Meet the Author

Jean-Claude Fournier is Professor at the University of Paris 12, France, and is a member of the Unite Mixte de Recherche Combinatoire et Optimisation (University of Paris 6 and CNRS) founded by Claude Berge.
Read More Show Less

Table of Contents

Introduction 17

Chapter 1. Basic Concepts 21

1.1 The origin of the graph concept 21

1.2 Definition of graphs 24

1.3 Subgraphs 28

1.4 Paths and cycles 29

1.5 Degrees 33

1.6 Connectedness 35

1.7 Bipartite graphs 36

1.8 Algorithmic aspects 37

1.9 Exercises 41

Chapter 2. Trees 45

2.1 Definitions and properties 45

2.2 Spanning trees 49

2.3 Application: minimum spanning tree problem 54

2.4 Connectivity 59

2.5 Exercises 66

Chapter 3. Colorings 71

3.1 Coloring problems 71

3.2 Edge coloring 71

3.3 Algorithmic aspects 73

3.4 The timetabling problem 75

3.5 Exercises 81

Chapter 4. Directed Graphs 83

4.1 Definitions and basic concepts 83

4.2 Acyclic digraphs 90

4.3 Arborescences 92

4.4 Exercises 95

Chapter 5. Search Algorithms 97

5.1 Depth-first search of an arborescence 97

5.2 Optimization of a sequence of decisions 103

5.3 Depth-first search of a digraph 109

5.4 Exercises 117

Chapter 6. Optimal Paths 119

6.1 Distances and shortest paths problems 119

6.2 Case of non-weighted digraphs: breadth-first search 120

6.3 Digraphs without circuits 125

6.4 Application to scheduling 128

6.5 Positive lengths 134

6.6 Other cases 142

6.7 Exercises 143

Chapter 7. Matchings 149

7.1 Matchings and alternating paths 149

7.2 Matchings in bipartite graphs 152

7.3 Assignment problem 156

7.4 Optimal assignment problem 164

7.5 Exercises 171

Chapter 8. Flows 173

8.1 Flows in transportation networks 173

8.2 The max-flow min-cut theorem 177

8.3 Maximum flow algorithm 180

8.4 Flow with stocks and demands 188

8.5 Revisiting theorems 191

8.6 Exercises 194

Chapter 9. Euler Tours 197

9.1 Euler trails and tours 197

9.2 Algorithms 201

9.3 The Chinese postman problem 207

9.4 Exercises 212

Chapter 10. Hamilton Cycles 215

10.1 Hamilton cycles 215

10.2 The traveling salesman problem 218

10.3 Approximation of a difficult problem 220

10.4 Approximation of themetric TSP 223

10.5 Exercises 234

Chapter 11. Planar Representations 237

11.1 Planar graphs 237

11.2 Other graph representations 242

11.3 Exercises 244

Chapter 12. Problems with Comments 247

12.1 Problem 1: A proof of k-connectivity 247

12.2 Problem2: An application to compiler theory 249

12.3 Problem3: Kernel of a digraph 251

12.4 Problem 4: Perfect matching in a regular bipartite graph 253

12.5 Problem5: Birkhoff-Von Neumann’s theorem 254

12.6 Problem 6: Matchings and tilings 256

12.7 Problem7: Strip mining 258

Appendix A. Expression of Algorithms 261

Appendix B. Bases of Complexity Theory 267

Bibliography 277

Index 279

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)