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Balanced colourings and the four colour conjecture


Author: J. A. Bondy
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
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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 [Enhancements On Off] (What's this?)

  • [1] C. Berge, Graphes et hypergraphes, Dunod, Paris, 1971. MR 0357171 (50:9639)
  • [2] F. Harary, Graph theory, Addison-Wesley, Reading, Mass., 1969. MR 41 #1566. MR 0256911 (41:1566)
  • [3] O. Ore, The four-color problem, Pure and Appl. Math., vol. 27, Academic Press, New York, 1967. MR 36 #74. MR 0216979 (36:74)
  • [4] J. Petersen, Die Theorie der regulären Graphen, Acta Math. 15 (1891), 193-220. MR 1554815

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0294173-4
Keywords: Balanced colouring, four colour conjecture, bridgeless cubic planar graphs, further, one-factor, even two-factor
Article copyright: © Copyright 1972 American Mathematical Society

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