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 Wilsons 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(s): Robin J. Wilson
Edition: 5
Publisher: Pearson
Year: 2010
Language: English
Pages: 184
City: Essex
Cover
Contents
Preface
Introduction
Chapter 1 - Definitions and Examples
1.1 - Definitions
1.2 - Examples
1.3 - Variations on a theme
1.4 - Three puzzles
Chapter 2 - Paths and Cycles
2.1 - Connectivity
2.2 - Eulerian graphs and digraphs
2.3 - Hamiltonian graphs and digraphs
2.4 - Applications
Chapter 3 - Trees
3.1 - Properties of trees
3.2 - Counting trees
3.3 - More applications
Chapter 4 - Planarity
4.1 - Planar graphs
4.2 - Euler's formula
4.3 - Dual graphs
4.4 - Graphs on other surfaces
Chapter 5 - Colouring Graphs
5.1 - Colouring vertices
5.2 - Chromatic polynomials
5.3 - Colouring maps
5.4 - The four-color theorem
5.5 - Colouring edges
Chapter 6 - Matching, Marriage, and Menger's Theorem
6.1 - Hall's 'marriage' theorem
6.2 - Menger's theorem
6.3 - Network flows
Chapter 7 - Matroids
7.1 - Introduction to matroids
7.2 - Examples of matroids
7.3 - Matroids and graphs
Appendix 1: Algorithms
Appendix 2: Table of numbers
List of symbols
Bibliography
Solutions to Selected Exercises
Introduction
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Index
