Which point sets admit a k-angulation?
Combinatorics
2013-01-24 v2 Computational Geometry
Abstract
For k >= 3, a k-angulation is a 2-connected plane graph in which every internal face is a k-gon. We say that a point set P admits a plane graph G if there is a straight-line drawing of G that maps V(G) onto P and has the same facial cycles and outer face as G. We investigate the conditions under which a point set P admits a k-angulation and find that, for sets containing at least 2k^2 points, the only obstructions are those that follow from Euler's formula.
Cite
@article{arxiv.1203.3618,
title = {Which point sets admit a k-angulation?},
author = {Michael S. Payne and Jens M. Schmidt and David R. Wood},
journal= {arXiv preprint arXiv:1203.3618},
year = {2013}
}
Comments
13 pages, 7 figures