On Triangle Contact Graphs-Reference-Cited by-同舟云学术

On Triangle Contact Graphs

Published:1994-06 Issue:2 Volume:3 Page:233-246
ISSN:0963-5483
Container-title:Combinatorics, Probability and Computing
language:en
Short-container-title:Combinator. Probab. Comp.

Author:

de Fraysseix Hubert,de Mendez Patrice Ossona,Rosenstiehl Pierre

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.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

Reference10 articles.

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2. [10] Tamassia R. and Tollis I. G. (1989) Tessellation representation of planar graphs. In: Proc. Twenty-Seventh Annual Allerton Conference on Communication, Control, and Computing 48–57.

3. [4] de Fraysseix H. , de Mendez P. O. and Pach J. (submitted) A streamlined depth-first search algorithm revisited.

4. [3] de Fraysseix H. and de Mendez P. O. (In preparation) On tree decompositions and angle marking of planar graphs.

5. [7] Mohar B. (To appear) Circle packings of maps in polynomial time.

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