Orienting Triangulations

Boris Albar (1) , Daniel Gonçalves (2) , Kolja Knauer (1, 3)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille
2 ALGCO - Algorithmes, Graphes et Combinatoire
3 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle

We prove that any triangulation of a surface different from the sphere and the projective plane admits an orientation without sinks such that every vertex has outdegree divisible by three. This confirms a conjecture of Barát and Thomassen and is a step towards a generalization of Schnyder woods to higher genus surfaces.

Mots clés: triangulations; orientations; surfaces

Mots clés: surfaces; orientations

Domaines: Informatique [cs]

Boris Albar, Daniel Gonçalves, Kolja Knauer. Orienting Triangulations. Journal of Graph Theory, 2016, 83 (4), pp.392-405. ⟨10.1002/jgt.22005⟩. ⟨hal-01457782⟩