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A Categorical Characterization of the Four Colour Theorem

Published online by Cambridge University Press:  20 November 2018

Barry Fawcett
Barry Fawcett*
Affiliation:
Dept. of Mathematics Statistics and Computing Science Dalhousie University Halifax, N.S. B3H 3J5
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Abstract

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The surjectivity of epimorphisms in the category of planar graphs and edge-preserving maps follows from and is implied by the Four Colour Theorem. The argument that establishes the equivalence is not combinatorially complex.

Keywords

05C15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 4 , 01 December 1986 , pp. 426 - 431
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Appel, K. and Haken, W. Every planar map is four colorable. Bull. A.M.S. 82 (1976), pp. 711–712.Google Scholar
2. Fawcett, B. A canonical factorization for graph homomorphisms. Can. J. Math. 29 (1977) pp. 738 —743.Google Scholar
3. Kelly, G. M. Monomorphisms, epimorphisms and pull-backs. J. Austral. Math. Soc. 9 (1969), pp. 124–142.Google Scholar
4. Ore, O. The Four Color Problem. Academic Press, New York, 1967.Google Scholar
5. Ringel, C. M. The intersection property of amalgamations. J. Pure Appl. Algebra 2 (1972), pp. 314–342.Google Scholar
6. Schubert, H. Categories. Springer Publications, Berlin 1972.Google Scholar