@inproceedings{Aichholzer2009PlaneGW,
title={Plane Graphs with Parity Constraints},
author={Oswin Aichholzer and Thomas Hackl and Michael Hoffmann and Alexander Pilz and G{\"u}nter Rote and Bettina Speckmann and Birgit Vogtenhuber},
booktitle={WADS},
year={2009}
}

Let S be a set of n points in general position in the plane. Together with S we are given a set of parity constraints, that is, every point of S is labeled either even or odd. A graph G on S satisfies the parity constraint of a point p ∈ S, if the parity of the degree of p in G matches its label. In this paper we study how well various classes of planar graphs can satisfy arbitrary parity constraints. Specifically, we show that we can always find a plane tree, a two-connected outerplanar graph… CONTINUE READING