Planar graphs and poset dimension

@article{Schnyder1989PlanarGA,
  title={Planar graphs and poset dimension},
  author={W. Schnyder},
  journal={Order},
  year={1989},
  volume={5},
  pages={323-343}
}
We view the incidence relation of a graph G=(V. E) as an order relation on its vertices and edges, i.e. a<Gb if and only of a is a vertex and b is an edge incident on a. This leads to the definition of the order-dimension of G as the minimum number of total orders on V ∪ E whose intersection is <G. Our main result is the characterization of planar graphs as the graphs whose order-dimension does not exceed three. Strong versions of several known properties of planar graphs are implied by this… Expand
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