On Triangle Contact Graphs
De Fraysseix, Hubert and Ossona de Mendez, Patrice and Rosenstiehl, Pierre (1997) On Triangle Contact Graphs. [Journal (Paginated)]
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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.
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