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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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References

[1]Andreev, E. M. (1970) On convex polyhedra in Lobacevskii spaces. Mat. Sb. 81 445–478.Google Scholar
[2]Di Battista, G., Eades, P., Tamassia, R. and Tollis, I. G. (1989) Algorithms for drawing planar graphs: an annotated bibliography. Tech. Rep. No. CS-89–09, Brown University, 1989.Google Scholar
[3]de Fraysseix, H. and de Mendez, P. O. (In preparation) On tree decompositions and angle marking of planar graphs.Google Scholar
[4]de Fraysseix, H., de Mendez, P. O. and Pach, J. (submitted) A streamlined depth-first search algorithm revisited.Google Scholar
[5]de Fraysseix, H., de Mendez, P. O. and Pach, J. (1993) Representation of planar graphs by segments. Intuitive Geometry (to appear).Google Scholar
[6]de Fraysseix, H., Pach, J. and Pollack, R. (1990) Small sets supporting Fary embeddings of planar graphs. Combinatorica 10 41–51.Google Scholar
[7]Mohar, B. (To appear) Circle packings of maps in polynomial time.Google Scholar
[8]Rosenstiehl, P., and Tarjan, R. E. (1986) Rectilinear planar layout and bipolar orientation of planar graphs. Discrete and Computational Geometry 1 343–353.CrossRefGoogle Scholar
[9]Schnyder, W. (1990) Embedding planar graphs on the grid. In: Proc. ACM-SIAM Symp. on Discrete Algorithms 138–148.Google Scholar
[10]Tamassia, R. and Tollis, I. G. (1989) Tessellation representation of planar graphs. In: Proc. Twenty-Seventh Annual Allerton Conference on Communication, Control, and Computing48–57.Google Scholar