Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Upper bounds for vertex degrees of planar $ 5$-chromatic graphs


Author: Lee W. Johnson
Journal: Trans. Amer. Math. Soc. 181 (1973), 53-59
MSC: Primary 05C15
MathSciNet review: 0321780
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Claude Berge, The theory of graphs and its applications, Translated by Alison Doig, Methuen & Co. Ltd., London; John Wiley & Sons Inc., New York, 1962. MR 0132541 (24 #A2381)
  • [2] A. Errera, Une contribution au problème des quatre couleurs, Bull. Soc. Math. France 53 (1925), 42–55 (French). MR 1504874
  • [3] M. Malec and Z. Skupień, On the maximal planar graphs and the four colour problem, Prace Mat. 12 (1969), 205–209. MR 0244101 (39 #5418)
  • [4] Oystein Ore, The four-color problem, Pure and Applied Mathematics, Vol. 27, Academic Press, New York-London, 1967. MR 0216979 (36 #74)
  • [5] 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.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 05C15

Retrieve articles in all journals with MSC: 05C15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0321780-8
PII: S 0002-9947(1973)0321780-8
Keywords: $ 4$-color problem, irreducible graphs, vertex degree, planar graphs
Article copyright: © Copyright 1973 American Mathematical Society