β Scribed by Robin J. Wilson
No coin nor oath required. For personal study only.
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 WilsonΒs 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
Title page
Contents
Preface to the fifth edition
Introduction
1 Definitions and examples
1.1 Definitions
1.2 Examples
1.3 Variations on a theme
1.4 Three puzzles
2 Paths and cycles
2.1 Connectivity
2.2 Eulerian graphs and digraphs
2.3 Hamiltonian graphs and digraphs
2.4 Applications
3 Trees
3.1 Properties of trees
3.2 Counting trees
3.3 More applications
4 Planarity
4.1 Planar graphs
4.2 Euler's formula
4.3 Dual graphs
4.4 Graphs on other surfaces
5 Colouring graphs
5.1 Colouring vertices
5.2 Chromatic polynomials
5.3 Colouring maps
5.4 The four-colour theorem
5.5 Colouring edges
6 Matching, marriage and Menger's theorem
6.1 Hall's marriage theorem
6.2 Mengers theorem
6.3 Network flows
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
Index
π SIMILAR VOLUMES
Graph Theory has recently 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. This book provides a comprehensive introduction to the subject.
Graph Theory has recently 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. This book provides a comprehensive introduction to the subject.
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