Orienting triangulations

2014/12/16 by Albar, Boris, Gonçalves, Daniel, Knauer, Kolja
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.4979

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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