Pre-triangulations and liftable complexes
O. Aichholzer, F. Aurenhammer, and T. Hackl
We introduce the concept of pre-triangulations, a relaxation of triangulations
that goes beyond the frequently used concept of pseudo-triangulations.
Pre-triangulations turn out to be more natural than pseudo-triangulations in
certain cases. We show that pre-triangulations arise in three different
contexts: In the characterization of polygonal complexes that are liftable to
three-space in a strong sense, in flip sequences for general polygonal
complexes, and as graphs of maximal locally convex functions.
Reference: O. Aichholzer, F. Aurenhammer, and T. Hackl.
Pre-triangulations and liftable complexes.
Discrete & Computational Geometry, 38:701-725, 2007.