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Elegant odd rings and non-planar graphs

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Combinatorial Mathematics VIII

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 884))

Abstract

We prove that a graph is non-planar if and only if it contains a strict elegant odd ring.

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References

  1. K. Kuratowski, Sur le probleme des courbes gauches en topologie, Fund. Math. 15 (1930) 271–283.

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  2. C.H.C. Little, A Conjecture About Circuits In Planar Graphs, Combinatorial Mathematics III, Lecture Notes in Mathematics, Springer, New York 452 (1975), 171–175.

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  3. C.H.C. Little, A Theorem On Planar Graphs, Combinatorial Mathematics IV, Lecture Notes in Mathematics, Springer, New York 560 (1976), 136–141.

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  4. K. Wagner, Ueber eine Eigenschaft der ebenen Komplexe, Math. Ann. 114 (1937), 570–590.

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Kevin L. McAvaney

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© 1981 Springer-Verlag

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Holton, D.A., Little, C.H.C. (1981). Elegant odd rings and non-planar graphs. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091823

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  • DOI: https://doi.org/10.1007/BFb0091823

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10883-2

  • Online ISBN: 978-3-540-38792-3

  • eBook Packages: Springer Book Archive

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