Hostname: page-component-76c49bb84f-lvxqv Total loading time: 0 Render date: 2025-07-13T08:45:48.272Z Has data issue: false hasContentIssue false
  • English
  • Français

Short Proof of a Map-Colour Theorem

Published online by Cambridge University Press:  20 November 2018

G. A. Dirac
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Heawood (3) showed that for h > 1 the countries of any map on a surface of connectivity h = 3 − x can be coloured using at most

colours. In a previous paper (1)1 proved the following

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 225 - 226
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Dirac, G. A., Map-colour theorems, Can. J. Math., 4 (1952), 480–490.Google Scholar
2. Dirac, G. A., A theorem of R. L. Brooks and a conjecture of H. Hadwiger, Proc. London Math. Soc. (3), 7 (1957).Google Scholar
3. Heawood, P. J., Map-colour theorem, Quart. J. Math., 24 (1890), 332–338.Google Scholar