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On Triangle Contact Graphs†

Published online by Cambridge University Press:  12 September 2008

Hubert de Fraysseix ,
Patrice Ossona de Mendez  and
Pierre Rosenstiehl
Hubert de Fraysseix
Affiliation:
CNRS, EHESS, 54 Boulevard Raspail, 75006, Paris, France
Patrice Ossona de Mendez
Affiliation:
CNRS, EHESS, 54 Boulevard Raspail, 75006, Paris, France
Pierre Rosenstiehl
Affiliation:
CNRS, EHESS, 54 Boulevard Raspail, 75006, Paris, France
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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-or 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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 2 , June 1994 , pp. 233 - 246
Copyright
Copyright © Cambridge University Press 1994

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