On Triangle Contact Graphs

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

1 CAMS - Centre d'Analyse et de Mathématique sociales

It is proved that any plane graph may be represented by a triangle contact system, that is a collection of triangular disks which are disjoint except at contact points, each contact point being a node of exactly one triangle. Representations using contacts of T- of Y-shaped objects follow. Moreover, there is a one-to-one mapping between all the triangular contact representations of a maximal plane graph and all its partitions into three Schnyder trees.

Domaines: Combinatoire [math.CO]

Hubert de Fraysseix, Patrice Ossona de Mendez, Pierre Rosenstiehl. On Triangle Contact Graphs. Bela Bollobas. Combinatorics, Geometry and Probability, Cambridge University Press, pp.165-178, 1997. ⟨hal-00008999⟩