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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 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 NP-complete to decide whether there exists a triangulation of H that satisfies all parity constraints
Originalsprache | englisch |
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Seiten (von - bis) | 47-69 |
Fachzeitschrift | Graphs and Combinatorics |
Jahrgang | 30 |
Ausgabenummer | 1 |
DOIs | |
Publikationsstatus | Veröffentlicht - 2014 |
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Theoretical
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