Nodally 3-connected planar graphs and convex combination mappings
Computational Geometry
2007-08-08 v1
Abstract
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.
Cite
@article{arxiv.0708.0964,
title = {Nodally 3-connected planar graphs and convex combination mappings},
author = {Colm O Dunlaing},
journal= {arXiv preprint arXiv:0708.0964},
year = {2007}
}
Comments
27 pages Latex, 11 postscript figures