Eric Colin De Verdière - Directeur de recherche CNRS, Examinateur
Victor Chepoi - Professeur, Université Aix-Marseille, Examinateur
Stefan Felsner - Professeur, TU Berlin, Rapporteur
Marc Noy - Professeur, UPC Barcelone, Rapporteur
Gilles Schaeffer - Directeur de recherche CNRS, Rapporteur
Andras Sebo - Directeur de recherche CNRS, Examinateur
Résumé :
Schnyder woods are particularly elegant combinatorial structures with numerous applications concerning planar triangulations and more generally 3-connected planar maps. We propose a simple generalization of Schnyder woods from the plane to maps on orientable surfaces of any genus with a special emphasis on the toroidal case. We provide a natural partition of the set of Schnyder woods of a given map into distributive lattices depending on the surface homology. In the toroidal case we show the existence of particular Schnyder woods with some global properties that are useful for optimal encoding or graph drawing purpose.