@inproceedings{1cbdfc88186e49e790f28bdd1fe11cc8,
title = "Plane graphs with parity constraints",
abstract = "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, or a pointed pseudo-triangulation which satisfy all but at most three parity constraints. With triangulations we can satisfy about 2/3 of all parity constraints. In contrast, for a given simple polygon H with polygonal holes on S, we show that it is NP-complete to decide whether there exists a triangulation of H that satisfies all parity constraints.",
author = "O. Aichholzer and T. Hackl and M. Hoffmann and A. Pilz and G. Rote and B. Speckmann and B. Vogtenhuber",
year = "2009",
doi = "10.1007/978-3-642-03367-4\_2",
language = "English",
isbn = "978-3-642-03366-7",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "13--24",
editor = "F. Dehne and M. Gavrilova and J.-R. Sack and C.D. T{\'o}th",
booktitle = "Algorithms and Data Structures (Proceedings 11th International Workshop, WADS 2009, Banff, Alberta, Canada, August 21-23, 2009)",
address = "Germany",
}