Orienting Triangulations

Boris Albar 1 Daniel Gonçalves 1 Kolja Knauer 2, 3
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
3 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle
LIS - Laboratoire d'Informatique et Systèmes
Abstract : 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.
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Boris Albar, Daniel Gonçalves, Kolja Knauer. Orienting Triangulations. Journal of Graph Theory, Wiley, 2016, 83 (4), pp.392-405. ⟨10.1002/jgt.22005⟩. ⟨hal-01457782⟩

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