Orienting triangulations

Boris Albar 1 Daniel Gonçalves 1 Kolja Knauer 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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 Bara ́t 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. EuroCG: European Workshop on Computational Geometry, Mar 2015, Ljubljana, Slovenia. ⟨lirmm-01264309⟩

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