Matching edges and faces in polygonal partitions

Authors:
O. Aichholzer;F. Aurenhammer;P. Gonzalez-Nava;T. Hackl;C. Huemer;F. Hurtado;H. Krasser;S. Ray;B. Vogtenhuber
Affiliations:
University of Technology, Graz, Austria;University of Technology, Graz, Austria;University of Technology, Graz, Austria;University of Technology, Graz, Austria;Universitat Politecnica de Catalunya, Barcelona, Spain;Universitat Politecnica de Catalunya, Barcelona, Spain;University of Technology, Graz, Austria;Max-Planck-Institut Informatik, Saarbrücken, Germany;University of Technology, Graz, Austria
Venue:
Computational Geometry: Theory and Applications
Year:
2008

Citing 6
Cited 1

Power diagrams: properties, algorithms and applications

SIAM Journal on Computing
Bounding functions and rigid graphs

SIAM Journal on Discrete Mathematics
Embedding planar graphs on the grid

SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
A combinatorial approach to planar non-colliding robot arm motion planning

FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Pseudotriangulations from Surfaces and a Novel Type of Edge Flip

SIAM Journal on Computing
Planar minimally rigid graphs and pseudo-triangulations

Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003

Large Bichromatic Point Sets Admit Empty Monochromatic 4-Gons

SIAM Journal on Discrete Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We define general Laman (count) conditions for edges and faces of polygonal partitions in the plane. Several well-known classes, including k-regular partitions, k-angulations, and rank-k pseudo-triangulations, are shown to fulfill such conditions. As an implication, non-trivial perfect matchings exist between the edge sets (or face sets) of two such structures when they live on the same point set. We also describe a link to spanning tree decompositions that applies to quadrangulations and certain pseudo-triangulations.