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A Categorical Characterization of the Four Colour Theorem

  • Barry Fawcett (a1)

Abstract

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.

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Copyright

References

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1. Appel, K. and Haken, W. Every planar map is four colorable. Bull. A.M.S. 82 (1976), pp. 711712.
2. Fawcett, B. A canonical factorization for graph homomorphisms. Can. J. Math. 29 (1977) pp. 738 —743.
3. Kelly, G. M. Monomorphisms, epimorphisms and pull-backs. J. Austral. Math. Soc. 9 (1969), pp. 124142.
4. Ore, O. The Four Color Problem. Academic Press, New York, 1967.
5. Ringel, C. M. The intersection property of amalgamations. J. Pure Appl. Algebra 2 (1972), pp. 314342.
6. Schubert, H. Categories. Springer Publications, Berlin 1972.
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A Categorical Characterization of the Four Colour Theorem

  • Barry Fawcett (a1)

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