Geodesic
Lattice structures from planar graphs
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the first part of the paper. In the second part the theorem is applied to show that interesting combinatorial sets related to a planar graph have lattice structure: Eulerian orientations, spanning trees and Schnyder woods. For the Schnyder wood application some additional theory has to be developed. In particular it is shown that a Schnyder wood for a planar graph induces a Schnyder wood for the dual.
DOI : 10.37236/1768
Classification : 05C10, 68R10, 06A07
Mots-clés : planar graph, distributive lattice, Eulerian orientations, spanning trees, Schnyder woods 
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     author = {Stefan Felsner},
     title = {Lattice structures from planar graphs},
     journal = {The electronic journal of combinatorics},
     year = {2004},
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     number = {1},
     doi = {10.37236/1768},
     zbl = {1056.05039},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1768/}
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Stefan Felsner. Lattice structures from planar graphs. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1768

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