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Matching Edges and Faces in Polygonal Partitions O. Aichholzer 1 F. Aurenhammer 2 P. GonzalezNava 3 T. Hackl 4 C. Huemer 5 F. Hurtado 6
 

Summary: Matching Edges and Faces in Polygonal Partitions
O. Aichholzer 1 F. Aurenhammer 2 P. Gonzalez­Nava 3 T. Hackl 4 C. Huemer 5 F. Hurtado 6
H. Krasser 7 S. Ray 8 B. Vogtenhuber 9
Abstract
We define general Laman (count) conditions for edges
and faces of polygonal partitions in the plane. Several
well­known classes, including k­regular partitions,
k­angulations, and rank­k pseudo­triangulations, are
shown to fulfill such conditions. As a consequence,
non­trivial 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 pseudo­triangulations.
1 Introduction
There exist several results [2] concerning matchings be­
tween the edges (or triangles) in two given triangula­
tions on top of the same point set S. For example,
for any two triangulations T 1 and T 2 of S, we can pair
each edge e 1 2 T 1 with an edge e 2 2 T 2 such that either

  

Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz

 

Collections: Computer Technologies and Information Sciences