Graphs, Colourings and the Four-Colour Theorem - Rilegato

Wilson, Robert A.

Rilegato

ISBN 10: 0198510616 ISBN 13: 9780198510611

Casa editrice: OUP Oxford, 2002

Riassunto

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.

Su questo libro

Recensione:

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)

Contenuti:

• 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

Su questa edizione

• Editore: OUP Oxford
• Data di pubblicazione: 2002
• ISBN 10: 0198510616
• ISBN 13: 9780198510611
• Rilegatura: Copertina rigida
• Numero di pagine: 150