Graphs, Colourings and the Four-Colour Theorem
Synopsis 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 part of the subject now known as graph theory. This volume 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. The text covers basic graph theory, Euler's polyhedral formula, and the first published false "proof" of the four-colour theorem.