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Graphs, Colourings and the Four-Colour Theorem - Robert A. Wilson

Graphs, Colourings and the Four-Colour Theorem

Hardcover

Published: 1st April 2002
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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. The Mathematical Gazette ... it will please every reader. And last but not least, it is a thin book, which will not eat much space in your library; the contents to weight ratio is well above the average. EMS ... a gentle introduction to graph theory ... provides a nice overview, and many details, of various approaches to the four-colour problem ... it has a place on the shelf of the professional graph theorist ... the book has much to recommend it. Zentralblatt MATH

Preface Part I - Graphs, Maps and the four-colour theorem1: Introduction 2: Basic Graph Theory 3: Applications of Euler's formula 4: Kempe's approach Part II - Related Topics5: Other approaches to the four-colour theorem 6: Maps on surfaces with holes 7: Kuratowski's theorem 8: Colouring non-planar graphs PArt III - How to prove the four-colour theorem9: Overview 10: Reducibility 11: Discharging Bibliography Index

ISBN: 9780198510611
ISBN-10: 0198510616
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 150
Published: 1st April 2002
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.1 x 16.1  x 1.4
Weight (kg): 0.35