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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Upper bounds for vertex degrees of planar $5$-chromatic graphs
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by Lee W. Johnson PDF
Trans. Amer. Math. Soc. 181 (1973), 53-59 Request permission

Abstract:

Upper bounds are given for the degrees of vertices in planar $5$-chromatic graphs. Some inequalities are derived for irreducible graphs which restrict the type of planar graphs that can be irreducible.
References
  • Claude Berge, The theory of graphs and its applications, Methuen & Co., Ltd., London; John Wiley & Sons, Inc., New York, 1962. Translated by Alison Doig. MR 0132541
  • A. Errera, Une contribution au problème des quatre couleurs, Bull. Soc. Math. France 53 (1925), 42–55 (French). MR 1504874, DOI 10.24033/bsmf.1080
  • M. Malec and Z. Skupień, On the maximal planar graphs and the four colour problem, Prace Mat. 12 (1969), 205–209. MR 0244101
  • Oystein Ore, The four-color problem, Pure and Applied Mathematics, Vol. 27, Academic Press, New York-London, 1967. MR 0216979
  • O. Ore and G. Stemple, Numerical methods in the four color problem, Recent Progress in Combinatorics (Proc. Third Waterloo Conf. on Combinatorics, 1968), Academic Press, New York, 1969.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 181 (1973), 53-59
  • MSC: Primary 05C15
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0321780-8
  • MathSciNet review: 0321780