A Categorical Characterization of the Four Colour Theorem
Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 426-431

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1986-067-8
Mots-clés : 05C15
Fawcett, Barry. A Categorical Characterization of the Four Colour Theorem. Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 426-431. doi: 10.4153/CMB-1986-067-8
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[1] 1. Appel, K. and Haken, W. Every planar map is four colorable. Bull. A.M.S. 82 (1976), pp. 711–712. Google Scholar

[2] 2. Fawcett, B. A canonical factorization for graph homomorphisms. Can. J. Math. 29 (1977) pp. 738 —743. Google Scholar

[3] 3. Kelly, G. M. Monomorphisms, epimorphisms and pull-backs. J. Austral. Math. Soc. 9 (1969), pp. 124–142. Google Scholar

[4] 4. Ore, O. The Four Color Problem. Academic Press, New York, 1967. Google Scholar

[5] 5. Ringel, C. M. The intersection property of amalgamations. J. Pure Appl. Algebra 2 (1972), pp. 314–342. Google Scholar

[6] 6. Schubert, H. Categories. Springer Publications, Berlin 1972. Google Scholar

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