Balanced colourings and the four colour conjecture
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- by J. A. Bondy PDF
- Proc. Amer. Math. Soc. 33 (1972), 241-244 Request permission
Abstract:
A conjectured property of bridgeless cubic planar graphs is shown to be equivalent to the four colour conjecture. In establishing this equivalence use is made of the König-Hall theorem on the existence of one-factors in bipartite graphs.References
- Claude Berge, Graphes et hypergraphes, Collection Dunod Université, Série Violette, No. 604, Dunod, Paris-Brussels-Montreal, Que., 1973 (French). Deuxième édition. MR 0357171
- Frank Harary, Graph theory, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London 1969. MR 0256911
- Oystein Ore, The four-color problem, Pure and Applied Mathematics, Vol. 27, Academic Press, New York-London, 1967. MR 0216979
- Julius Petersen, Die Theorie der regulären graphs, Acta Math. 15 (1891), no. 1, 193–220 (German). MR 1554815, DOI 10.1007/BF02392606
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 241-244
- MSC: Primary 05C15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294173-4
- MathSciNet review: 0294173