 
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
