Abstract
In October 1971 the combinatorial world was swept by the rumour that the notorious Four Colour Problem had at last been solved, - that with the help of a computer it had been demonstrated that any map in the plane can be coloured with at most four - colours so that no two countries with a common boundary line are given the same colour.
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References
G. D. Birkhoff, The Reducibility of Maps, Amer. J. Math., 35 (1913), 115–128.
P. J. Heawood, Map-colour Theorem, Quart. J. Math. Oxford, Ser. 24 (1890), 322–338.
H. Heesch, Untersuchungen zum Vierfarbenproblem, Hochschulskripten 810/810a/810b, Mannheim 1969.
A. B. Kempe, On the Geographical Problem of the Four Colours, Amer. J. Math., 2 (1879), 193–200.
O. Ore, The Four-color Problem, Academic Press, New York, 1967.
O. Ore and J. Stemple, Numerical Calculations on the Four- color Problem, J. Combinatorial Theory, 8 (1970), 65–78.
T. L. Saaty, Thirteen Colorful Variations on Guthrie’s Four-color Conjecture. Amer. Math. Monthly, 79 (1972), 2–43.
W. T. Tutte, On the Four Colour Conjecture, Proc. London Math. Soc., 50 (1948), 137–149.
C. E. Winn, On the Minimum Number of Polygons in an Irreducible Map, Amer. J. Math., 62 (1940), 406–416.
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© 1992 Birkhäuser Boston
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Whitney, H., Tutte, W.T. (1992). Kempe Chains and the Four Colour Problem. In: Eells, J., Toledo, D. (eds) Hassler Whitney Collected Papers. Contemporary Mathematicians. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2972-8_13
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DOI: https://doi.org/10.1007/978-1-4612-2972-8_13
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