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On Triangle Contact Graphs

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00008999
Contributor : Patrice Ossona de Mendez Connect in order to contact the contributor
Submitted on : Wednesday, September 21, 2005 - 6:16:58 PM
Last modification on : Friday, July 17, 2020 - 8:53:32 AM

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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⟩

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