Graphs, Colourings and the Four-Colour Theorem
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Product details:
- Publisher OUP Oxford
- Date of Publication 24 January 2002
- ISBN 9780198510628
- Binding Paperback
- No. of pages150 pages
- Size 233x156x8 mm
- Weight 225 g
- Language English
- Illustrations numerous figures 0
Categories
Short description:
This textbook for mathematics undergraduates, graduates and researchers discusses the proof of the four-colour theorem - one of the most famous of the long-standing mathematical problems solved in the 20th century.
MoreLong description:
The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours.
The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory.
The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem.
Part I covers basic graph theory, Euler's polyhedral formula, and the first published false `proof' of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem.
This is a lively and readable account of one of the great problems of mathematics and its solution and can be recommended to all readers who are interested and prepared to make the effort to follow it.
Table of Contents:
Preface
Introduction
Basic Graph Theory
Applications of Euler's formula
Kempe's approach
Other approaches to the four-colour theorem
Maps on surfaces with holes
Kuratowski's theorem
Colouring non-planar graphs
Overview
Reducibility
Discharging
Bibliography
Index
