Regular odd rings and non-planar graphs

Abstract

In a previous paper we have announced that a graph is non-planar if and only if it contains a maximal, strict, compact, odd ring. Little has conjectured that the compactness condition may be removed. Chernyak has now published a proof of this conjecture. However, it is difficult to test a ring for maximality. In this paper we show that for odd rings of size five or greater, the condition of maximality may be replaced by a new one called regularity. Regularity is an easier condition to diagnose than is maximality.

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References

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Holton, D.A., Little, C.H.C. Regular odd rings and non-planar graphs. Combinatorica 2, 149–152 (1982). https://doi.org/10.1007/BF02579313

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AMS subject classification (1980)

  • 05 C 10
  • 05 C 38