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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A short proof of Mac Lane’s planarity theorem
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by P. V. O’Neil PDF
Proc. Amer. Math. Soc. 37 (1973), 617-618 Request permission

Abstract:

This note gives a short and elementary proof of Mac Lane’s theorem on the embedding of graphs in a 2-sphere.
References
  • Frank Harary, Graph theory, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London 1969. MR 0256911
    • C. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271-283.
  • Solomon Lefschetz, Planar graphs and related topics, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1763–1765. MR 189011, DOI 10.1073/pnas.54.6.1763
    • S. Mac Lane, A combinatorial condition for planar graphs, Fund. Math. 28 (1937), 22-32.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 37 (1973), 617-618
  • MSC: Primary 05C10
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0313098-X
  • MathSciNet review: 0313098