On flips in triangulations
Prosenjit K. Bose · 2005
We review a selection of results concerning edge flips in triangulations concentrating mainly on various aspects of the following problem: Given two different triangulations, how many edge flips are necessary and sufficient to transform one triangulation into another. We study the problem both from a combinatorial perspective (where only a combinatorial embedding of the triangulation is specified) and a geometric perspective (where the triangulation is embedded in the plane, vertices are points and edges are straight-line segments). We highlight both the similarities and differences of the two settings as well as outline some open problems.