A History of Flips in Combinatorial Triangulations
Prosenjit Bose, Sander Verdonschot
TL;DR
This paper surveys the long-standing problem of determining the minimum number of edge flips needed to transform one combinatorial triangulation into another, providing detailed proofs and historical context.
Contribution
It offers a comprehensive survey with full proofs of the various approaches to solving the edge flip problem in combinatorial triangulations.
Findings
Summarizes key results and bounds on edge flip counts
Provides detailed proofs of major theorems
Highlights open problems and future directions
Abstract
Given two combinatorial triangulations, how many edge flips are necessary and sufficient to convert one into the other? This question has occupied researchers for over 75 years. We provide a comprehensive survey, including full proofs, of the various attempts to answer it.
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