Plane graphs with parity constraints

O. Aichholzer, T. Hackl, M. Hoffmann, A. Pilz, G. Rote, B. Speckmann, B. Vogtenhuber

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

8 Citations (Scopus)


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.
Original languageEnglish
Title of host publicationAlgorithms and Data Structures (Proceedings 11th International Workshop, WADS 2009, Banff, Alberta, Canada, August 21-23, 2009)
EditorsF. Dehne, M. Gavrilova, J.-R. Sack, C.D. Tóth
Place of PublicationBerlin
ISBN (Print)978-3-642-03366-7
Publication statusPublished - 2009

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743


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