Lattice Structures from Planar Graphs

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.

• Type: Journal
• Year: 2004
• Where: COMBINATORICS
• Authors: Stefan Felsner
• Keywords: COMBINATORICS 2004, Interesting Combinatorial Sets, Planar Graph, Schnyder Wood