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Does contraction preserve triangular meshes?

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Abstract

A triangular graph is a planar graph in which each face is a 3-cycle, except possibly for the exterior face, and without articulation nodes. The embedding of a triangular graph in the plane is called a triangular mesh. More generally, a triangular graph with multiple contours is a planar graph without articulation nodes in which each face is a 3-cycle, except possibly for a fixed number of them. A contraction along an edge in a graph is the result of identifying the two endpoints of the edge. In this paper a necessary and sufficient condition is shown for which triangularity (possibly with multiple contours) is preserved after contraction. Moreover, when a licit contraction is performed, the question to answer is whether or not it is possible to derive the embedding of the contracted triangular graph from the original triangular mesh by redrawing only around the contraction zone.

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Author information

Authors and Affiliations

  1. CEA/LV, F-94195, Villeneuve St Georges Cedex, France

    P. Ciarlet Jr

  2. Branche CEA-Défense, CISI, BP 28, F-91192, Gif sur Yvette Cedex, France

    F. Lamour

Authors
  1. P. Ciarlet Jr
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  2. F. Lamour
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Additional information

Communicated by C. Brezinski

Part of this work was done when the author was in his sabbatical year at the University of California at Los Angeles.

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Ciarlet, P., Lamour, F. Does contraction preserve triangular meshes?. Numer Algor 13, 201–223 (1996). https://doi.org/10.1007/BF02207695

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  • DOI: https://doi.org/10.1007/BF02207695

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