# A History of Flips in Combinatorial Triangulations

@inproceedings{Bose2011AHO,
title={A History of Flips in Combinatorial Triangulations},
author={Prosenjit Bose and Sander Verdonschot},
booktitle={EGC},
year={2011}
}
• Published in EGC 1 June 2012
• Mathematics
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.
18 Citations
A Lower Bound on the Diameter of the Flip Graph
The diameter of the flip graph is shown to be at least $\frac{7n}{3} + \Theta(1)$, improving upon the previous $2n + Theta (1)$ lower bound.
Modular flip-graphs of one-holed surfaces
• Mathematics
Eur. J. Comb.
• 2018
Transforming plane triangulations by simultaneous diagonal flips
• Mathematics, Computer Science
Inf. Process. Lett.
• 2021
Flipping edge-labelled triangulations
• Computer Science, Mathematics
Comput. Geom.
• 2018
Edge Flips in Combinatorial Triangulations
This project will investigate a topic that has fascinated geometers for many years: the flip graph of triangulations, which is considered abstract unlabeled (i.e. isomorphism classes of) triangulation.
Construction of acyclically 4-colourable planar triangulations with minimum degree 4
• Mathematics
Int. J. Comput. Math.
• 2019
This paper describes a method for constructing all 4-connected acyclically 4-colourable planar triangulations that have exactly four odd-vertices, except the ones that contain no adjacent odd-vertedices.
Flip Distances Between Graph Orientations
• Mathematics
Algorithmica
• 2020
It is proved that deciding whether the flip distance between two $\alpha$-orientations of a planar graph $G$ is at most two is \NP-complete, and this also holds in the special case of perfect matchings, where flips involve alternating cycles.

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A derivation in a transformational system such as a graph grammar may be redundant in the sense that the exact order of the transformations may not affect the final outcome; all that matters is that