The Ringel-Youngs theorem, known before its proof as the Heawood conjecture, gives the minimum number of colors needed to color every map on a surface of a given genus. For surfaces of genus 0, 1, 2, 3 and higher the required number of colors follows a formula giving 4, 7, 8, 9, 10 and so on; P. J. Heawood proposed the conjecture in 1890, and Gerhard Ringel and J. W. T. Youngs proved it in 1968, with the Klein bottle standing as the formula's sole exception, since Philip Franklin had shown in 1930 that it needs only six colors rather than the seven the general formula predicts.
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Statement Form Ringel-Youngs Theorem
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Source Heawood conjecture (Wikipedia)
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Source Ringel-Youngs Theorem (Wikipedia)
Source Ringel-Youngs Theorem (Wikipedia)
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Source Heawood conjecture (Wikipedia)
Source Heawood conjecture (Wikipedia)
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1. Heawood conjecture (Wikipedia)
- [The Heawood conjecture, restated as the Ringel-Youngs theorem] proven in 1968 by Gerhard Ringel and J.W.T. Youngs
- In Branch: Graph Theory, Lead sentence
Proved By: Gerhard Ringel, Lead
The conjecture was formulated in 1890 by P.J. Heawood and proven in 1968 by Gerhard Ringel and J.W.T. Youngs.
Proved By: J. W. T. Youngs, Lead
The conjecture was formulated in 1890 by P.J. Heawood and proven in 1968 by Gerhard Ringel and J.W.T. Youngs.
In Group: Graph Theory, Lead section
In graph theory, the Heawood conjecture or Ringel-Youngs theorem
View the SourceRingel-Youngs Theorem (Wikipedia)
Principal Result Of: Gerhard Ringel, Lead sentence of the article on the result
Heawood and proven in 1968 by Gerhard Ringel and J.W.T.
Principal Result Of: J. W. T. Youngs, Lead sentence of the article on the result
Then the years in which the twelve cases were settled, and by whom, are the following: 1954, Ringel: case 5 1961, Ringel: cases 3, 7, 10 1963, Terry, Welch, Youngs: cases 0, 4 1964, Gustin, Youngs: case 1 1965, Gustin: case 9 1966, Youngs: case 6 1967, Ringel, Youngs: cases 2, 8, 11 The last seven sporadic exceptions were settled as follows: 1967, Mayer: cases 18, 20, 23 1968, Ringel, Youngs: cases 30, 35, 47, 59, and the conjecture was proved.
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