Introduction to Graph Theory

by Wilson, Robin J.

• ISBN13: 9780273728894
• ISBN10: 027372889X
• Edition: 5th
• Format: Paperback
• Copyright: 2010-05-20
• Publisher: Pearson

Summary

In recent years graph theory has emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. Robin Wilson's book has been widely used as a text for undergraduate courses in mathematics, computer science and economics, and as a readable introduction to the subject for non-mathematicians. The opening chapters provide a basic foundation course, containing definitions and examples, connectedness, Eulerian and Hamiltonian paths and cycles, and trees, with a range of applications. This is followed by two chapters on planar graphs and colouring, with special reference to the four-colour theorem. The next chapter deals with transversal theory and connectivity, with applications to network flows. A final chapter on matroid theory ties together material from earlier chapters, and an appendix discusses algorithms and their efficiency.

Author Biography

Robin Wilson is Emeritus Professor of Pure Mathematics at the Open University, and Emeritus Professor of Geometry at Gresham College, London. He is also a former Fellow in Mathematics at Keble College, Oxford University, and now teaches at Pembroke College. He has written and edited almost 40 books on graph theory, combinatorics, the history of mathematics, and music, and is very involved with the communication and popularisation of mathematics.

Table of Contents

Introduction

1. Definitions and examples
2. Paths and cycles
3. Trees
4. Planarity
5. Colouring graphs
6. Matching, marriage and Menger's theorem
7. Matroids

Appendix 1: Algorithms

Appendix 2: Table of numbers

List of symbols

Bibliography

Solutions to selected exercises

Index