Abstract
We give an alternate proof of Schnyder’s Theorem, that the incidence poset of a graph G has dimension at most three if and only if G is planar.
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References
Babai, L., Duffus, D.: Dimension and automorphism groups of lattices. Algebra Univers. 12, 279–289 (1981)
Brightwell, G., Trotter, W.T.: The order dimension of convex polytopes. SIAM J. Discrete Math. 6, 230–245 (1993)
Brightwell, G., Trotter, W.T.: The order dimension of planar maps. SIAM J. Discrete Math. 6, 515–528 (1997)
Castelli Aleardi, L., Fusy, E., Lewiner, T.: Schnyder woods for higher genus triangulated surfaces, with applications to encoding. Discrete Comput. Geom. 42, 489–516 (2009)
Felsner, S.: Convex drawings of planar graphs and the order dimension of 3-polytopes. Order 18, 19–37 (2001)
Felsner, S.: Geodesic embeddings and planar graphs. Order 20, 135–150 (2003)
Felsner, S., Trotter, W.T.: Posets and planar graphs. J. Graph Theory 49, 273–284 (2005)
Felsner, S., Zickfeld, F.: Schnyder woods and orthogonal surfaces. Discrete Comput. Geom. 40, 103–126 (2008)
de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10, 41–51 (1990)
Ossona de Mendez, P.: Geometric realization of simplicial complexes. Graph Drawing, Lect. Notes Comput. Sci. 5, 323–332 (1999)
Schnyder, W.: Planar graphs and poset dimension. Order 5, 323–343 (1989)
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Fidel Barrera-Cruz was partially supported by CONACYT, Project 209395/304106.
Penny Haxell was partially supported by NSERC.
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Barrera-Cruz, F., Haxell, P. A Note on Schnyder’s Theorem. Order 28, 221–226 (2011). https://doi.org/10.1007/s11083-010-9167-z
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DOI: https://doi.org/10.1007/s11083-010-9167-z