Orienting triangulations
classification
🧮 math.CO
keywords
admitsconfirmsconjecturedifferentdivisibleeverygeneralizationgenus
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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 Bar\'at and Thomassen and is a step towards a generalization of Schnyder woods to higher genus surfaces.
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