Introduction to Graph Theory

Description

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. 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