On Lattice Structures induced by Orientations.
Résumé
It is proved that the algebaric cocycles of orientations such that the number of positive arcs is prescribed on each cycle have a distributive lattice structure. By duality we deduce that orientations with prescribed indegrees also have a distributive lattice structure. Using simple bijections, these structures also applies to bipolar orientations of biconnected planar graphs and to Schnyder wood decompositions of maximal planar graphs.