Graphs, Colourings and the Four-colour Theorem
By (author) Robert A. Wilson
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Graphs, Colourings and the Four-colour Theorem by Robert A. Wilson
Book DescriptionThe 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.
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Book DetailsISBN: 9780198510628
(233mm x 156mm x 8mm)
Imprint: Oxford University Press
Publisher: Oxford University Press
Publish Date: 24-Jan-2002
Country of Publication: United Kingdom
Books By Author Robert A. Wilson
Genes and the Agents of Life, Paperback (September 2004)
This book undertakes to rethink the place of the individual in the biological sciences.
Boundaries of the Mind, Hardback (July 2004)
This 2004 book provides the foundations for the view that the mind extends beyond the boundary of the individual.
Graphs, Colourings and the Four-colour Theorem, Hardback (January 2002)
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.
MIT Encyclopedia of the Cognitive Sciences (MITECS), Paperback (October 2001)» View all books by Robert A. Wilson
A landmark, comprehensive reference work that represents the methodological and theoretical diversity of this changing field.
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