Orienting triangulations
  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. 
Boris Albar, Daniel Gon\c{c}alves, Kolja Knauer
math.CO