A short proof of a Gauss problem

  • H. de Fraysseix
  • P. Ossona de Mendez
Crossings and Planarity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)


The traversal of a self crossing closed plane curve, with points of multiplicity at most two, defines a double occurrence sequence.

C.F. Gauss conjectured (2] that such sequences could be characterized by their interlacement properties. This conjecture was proved by P. Rosenstiehl in 1976 [15]. We shall give here a simple self-contained proof of his characterization. This new proof relies on the D-switch operation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • H. de Fraysseix
    • 1
  • P. Ossona de Mendez
    • 1
  1. 1.CNRS UMR 0017, EHESSParisFrance

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