 
Summary: New Results on MWT Subgraphs
Oswin Aichholzer
Franz Aurenhammer
Reinhard Hainz
Institute for Theoretical Computer Science
Graz University of Technology
Klosterwiesgasse 32/2, A8010 Graz, Austria
email: foaich,aureng@igi.tugraz.ac.at
Abstract
Let P be a polygon in the plane. We disprove the conjecture that the socalled LMT
skeleton coincides with the intersection of all locally minimal triangulations, LMT (P ),
even for convex polygons P . We introduce an improved LMTskeleton algorithm which,
for any simple polygon P , exactly computes LMT (P ), and thus a larger subgraph of the
minimumweight triangulation MWT (P ). The algorithm achieves the same in the general
point set case provided the connectedness of the improved LMTskeleton, which is given
in allmost all practical instances.
We further observe that the skeleton of P is a subset of MWT (P ) for all values
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