Barycentric systems and stretchability

Hubert de Fraysseix (1) , Patrice Ossona de Mendez (1)

1 CAMS - Centre d'Analyse et de Mathématique sociales

Using a general resolution of barycentric systems we give a generalization of Tutte's theorem on convex drawing of planar graphs. We deduce a characterization of the edge coverings into pairwise non-crossing paths which are stretchable: such a system is stretchable if and only if each subsystem of at least two paths has at least 3 free vertices (vertices of the outer face of the induced subgraph which are internal to none of the paths of the subsystem). We also deduce that a contact system of pseudo-segments is stretchable if and only if it is extendible.

Domaines: Combinatoire [math.CO]

Hubert de Fraysseix, Patrice Ossona de Mendez. Barycentric systems and stretchability. Discrete Applied Mathematics, 2007, 155 (9), pp.1079-1095. ⟨10.1016/j.dam.2005.12.009⟩. ⟨hal-00147454⟩