Abstract
THE countries of a map are sometimes given colours in such a way that no two countries which have a common frontier line are coloured the same. Map-makers have long known empirically that four colours are sufficient to colour a map in this way, provided they are distributed correctly. In the nineteenth century, de Morgan and Cayley directed attention to this, and unsuccessful attempts were made to prove or disprove that any map drawn on the surface of a sphere or on a plane can be coloured, using at most four colours. This question, known as the four-colour problem, is to-day one of the most famous unsolved problems in mathematics. Heawood1 has proved that five colours are always sufficient.
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Heawood, P. J., Quart. J. Math., 24, 332 (1890).
Ibid. Also Hilbert and Cohn-Vossen, “Anschaulische Geometrie”, 297.
Canad. J. Math., and J. London Math. Soc., respectively.
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DIRAC, G. The Colouring of Maps. Nature 169, 664 (1952). https://doi.org/10.1038/169664a0
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DOI: https://doi.org/10.1038/169664a0
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