# Forbidding Edges between Points in the Plane to Disconnect the Triangulation Flip Graph

@article{Bigdeli2022ForbiddingEB, title={Forbidding Edges between Points in the Plane to Disconnect the Triangulation Flip Graph}, author={Reza Bigdeli and Anna Lubiw}, journal={ArXiv}, year={2022}, volume={abs/2206.02700} }

The ﬂip graph for a set P of points in the plane has a vertex for every triangulation of P , and an edge when two triangulations diﬀer by one ﬂip that replaces one triangulation edge by another. The ﬂip graph is known to have some connectivity properties: (1) the ﬂip graph is connected; (2) connectivity still holds when restricted to triangulations containing some constrained edges between the points; (3) for P in general position of size n , the ﬂip graph is (cid:100) n 2 − 2 (cid:101…

## One Citation

### Connectivity Properties of the Flip Graph After Forbidding Triangulation Edges

- Mathematics
- 2022

The flip graph for a set P of points in the plane has a vertex for every triangulation of P , and an edge when two triangulations differ by one flip that replaces one triangulation edge by another.…

## References

SHOWING 1-10 OF 27 REFERENCES

### The Edge-flipping Distance of Triangulations

- Computer Science, MathematicsJ. Univers. Comput. Sci.
- 1996

An upper bound on the edge-flipping distance between triangulation of a general finite set of points in the plane is established by showing that no more edge-Flipping operations than the number of intersections between the edges of two triangulations are needed to transform these triangulated into another, and an algorithm is presented that computes such a sequence of edge- flipping operations.

### A Proof of the Orbit Conjecture for Flipping Edge-Labelled Triangulations

- MathematicsSoCG
- 2017

The Orbit Conjecture is proved, i.e. that all labels can be simultaneously mapped to their destination if and only if each label individually can be mapped to its destination.

### Flip distance between triangulations of a planar point set is APX-hard

- MathematicsComput. Geom.
- 2014

### Flipping Edges in Triangulations

- Mathematics, Computer ScienceSCG '96
- 1996

It is proved that any triangulation of a set of n points in general position contains at least $\lceil (n-4)/2 \rceil$ edges that can be flipped.

### Random lattice triangulations: structure and algorithms

- MathematicsSTOC '13
- 2013

These are apparently the first rigorous quantitative results on spatial mixing properties and dynamics of random lattice triangulations.

### Flip Distance Between Two Triangulations of a Point Set is NP-complete

- Computer Science, MathematicsCCCG
- 2012

### Rotation distance, triangulations, and hyperbolic geometry

- Computer ScienceSTOC '86
- 1986

A tight bound is established on the maximum rotation distance between two A2-node trees for all large n, using volumetric arguments in hyperbolic 3-space, and is given on the minimum number of tetrahedra needed to dissect a polyhedron in the worst case.

### Happy endings for flip graphs

- MathematicsSCG '07
- 2007

We show that the triangulations of a finite point set form a flip graph that can be embedded isometrically into a hypercube, if and only if the point set has no empty convex pentagon. Point sets of…

### Triangulations: Structures for Algorithms and Applications

- Mathematics
- 2010

Triangulations appear everywhere, from volume computations and meshing to algebra and topology. This book studies the subdivisions and triangulations of polyhedral regions and point sets and presents…