A characterization of planar graphs by trémaux orders

Abstract

A new characterization of planar graphs is stated in terms of an order relation on the vertices, called the Trémaux order, associated with any Trémaux spanning tree or Depth-First-Search Tree. The proof relies on the work of W. T. Tutte on the theory of crossings and the Trémaux algebraic theory of planarity developed by P. Rosenstiehl.

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de Fraysseix, H., Rosenstiehl, P. A characterization of planar graphs by trémaux orders. Combinatorica 5, 127–135 (1985). https://doi.org/10.1007/BF02579375

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AMS subject classification (1980)

  • 05 C 10
  • 57 M 15