A generalization of the $5$-color theorem
HTML articles powered by AMS MathViewer
- by Paul C. Kainen PDF
- Proc. Amer. Math. Soc. 45 (1974), 450-453 Request permission
Abstract:
We present a short topological proof of the $5$-color theorem using only the nonplanarity of ${K_6}$. As a bonus, we find that any graph which becomes planar upon the removal of 2 edges can be $5$-colored and that any graph which becomes planar when 5 edges are removed is $6$-colorable.References
- Philip Franklin, The four color problem, Scripta Math. 6 (1939), 149–156, 197–210. MR 1901
- Herbert Grötzsch, Zur Theorie der diskreten Gebilde. V. Beziehungen zwischen Vierkant- und Dreikantnetzen auf der Kugel, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 7 (1958), 353–358 (German). MR 116318 P. J. Heawood, Map colour theorem, Quart. J. Math. 24 (1890), 332-338.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 45 (1974), 450-453
- MSC: Primary 05C15
- DOI: https://doi.org/10.1090/S0002-9939-1974-0345861-4
- MathSciNet review: 0345861