English

Orienting triangulations

Combinatorics 2014-12-17 v1

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.

Keywords

Cite

@article{arxiv.1412.4979,
  title  = {Orienting triangulations},
  author = {Boris Albar and Daniel Gonçalves and Kolja Knauer},
  journal= {arXiv preprint arXiv:1412.4979},
  year   = {2014}
}
R2 v1 2026-06-22T07:33:18.581Z