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Zusatztext ... 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. Klappentext 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 allconceivable 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 afascinating 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 onspecific 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 ofKuratowski, 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. Zusammenfassung 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. Inhaltsverzeichnis Preface Part I - Graphs, Maps and the four-colour theorem 2: Basic Graph Theory 3: Applications of Euler's formula 4: Kempe's approach Part II - Related Topics 6: Maps on surfaces with holes 7: Kuratowski's theorem 8: Colouring non-planar graphs PArt III - How to prove the four-colour theorem 10: Reducibility 11: Discharging Bibliography Index ...
