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… 

Connectivity Properties of the Flip Graph After Forbidding Triangulation Edges

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

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

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

Flipping Edges in Triangulations

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

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

Flips in planar graphs

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

Rotation distance, triangulations, and hyperbolic geometry

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

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

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