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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A short proof of Mac Lane's planarity theorem


Author: P. V. O’Neil
Journal: Proc. Amer. Math. Soc. 37 (1973), 617-618
MSC: Primary 05C10
MathSciNet review: 0313098
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Abstract: This note gives a short and elementary proof of Mac Lane's theorem on the embedding of graphs in a 2-sphere.


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

  • [1] Frank Harary, Graph theory, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London, 1969. MR 0256911 (41 #1566)
  • [2] C. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271-283.
  • [3] Solomon Lefschetz, Planar graphs and related topics, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1763–1765. MR 0189011 (32 #6438)
  • [4] S. Mac Lane, A combinatorial condition for planar graphs, Fund. Math. 28 (1937), 22-32.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0313098-X
PII: S 0002-9939(1973)0313098-X
Keywords: Planar graphs, 2-fold complete set of circuits
Article copyright: © Copyright 1973 American Mathematical Society