Orienting triangulations

Published 16 Dec 2014 in math.CO | (1412.4979v1)

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 Bar\'at and Thomassen and is a step towards a generalization of Schnyder woods to higher genus surfaces.

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