Projects per year
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 twoconnected outerplanar graph, or a pointed pseudotriangulation that satisfy all but at most three parity constraints. For triangulations we can satisfy about 2/3 of the parity constraints and we show that in the worst case there is a linear number of constraints that cannot be fulfilled. In addition, we prove that for a given simple polygon H with polygonal holes on S, it is NPcomplete to decide whether there exists a triangulation of H that satisfies all parity constraints
Original language  English 

Pages (fromto)  4769 
Journal  Graphs and Combinatorics 
Volume  30 
Issue number  1 
DOIs  
Publication status  Published  2014 
Fields of Expertise
 Information, Communication & Computing
Treatment code (Nähere Zuordnung)
 Theoretical
Fingerprint
Dive into the research topics of 'Plane graphs with parity constraints'. Together they form a unique fingerprint.
Discrete and Computational Geometry
Hackl, T., Aigner, W., Pilz, A., Vogtenhuber, B., Kornberger, B. & Aichholzer, O.
1/01/05 → …
Project: Research area

FWF  ComPoSe  EuroGIAG_ErdösSzekeres type problems for colored point sets and compatible graphs
1/10/11 → 31/12/15
Project: Research project

FWF  CPGG  Combinatorial Problems on Geometric Graphs
Hackl, T.
1/09/11 → 31/12/15
Project: Research project