4-labelings and Grid Embeddings of Plane Quadrangulations

@article{Barrire20124labelingsAG,
title={4-labelings and Grid Embeddings of Plane Quadrangulations},
author={Lali Barri{\`e}re and Clemens Huemer},
journal={Discrete Mathematics},
year={2012},
volume={312},
pages={1722-1731}
}

We show that each quadrangulation on n vertices has a closed rectangle of influence drawing on the (n − 2) × (n − 2) grid. Further, we present a simple algorithm to obtain a straight-line drawing of a quadrangulation on the ⌈ n 2 ⌉ × ⌈ 3n 4 ⌉ grid. This is not optimal but has the advantage over other existing algorithms that it is not needed to add edges to the quadrangulation to make it 4-connected. The algorithm is based on angle labeling and simple face counting in regions analogous to… CONTINUE READING