Nodally 3-connected planar graphs and convex combination mappings

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A convex combination mapping of a planar graph is a plane mapping in which the external vertices are mapped to the corners of a convex polygon and every internal vertex is a proper weighted average of its neighbours. If a planar graph is nodally 3-connected or triangulated then every such mapping is an embedding (Tutte, Floater). We give a simple characterisation of nodally 3-connected planar graphs, and generalise the above result to any planar graph which admits any convex embedding.
27 pages Latex, 11 postscript figures

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Computational Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/135708

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.0964
 http://arxiv.org/abs/0708.0964

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arXiv