Diagonal flips in pseudo-triangulations on closed surfaces

Diagonal flips in outer-triangulations on closed surfaces

We show that any two outer-triangulations on the same closed surface can be transformed into each other by a sequence of diagonal ips, up to isotopy, if they have a su6ciently large and equal number of vertices. c © 2002 Elsevier Science B.V. All rights reserved.

Diagonal flips in triangulations of surfaces

It will be shown that any two triangulations of a closed surface can be transformed into each other by flipping diagonals in quadrilaterals if they have a sufficiently large and equal number of vertices.

Diagonal Flips of Triangulations on Surfaces , a Survey

Diagonal Flips in Hamiltonian Triangulations on the Sphere

In this paper, we shall prove that any two Hamiltonian triangulations on the sphere with n 5 vertices can be transformed into each other by at most 4n 20 diagonal flips, preserving the existence of Hamilton cycles. Moreover, using this result, we shall prove that at most 6n 30 diagonal flips are needed for any two triangulations on the sphere with n vertices to transform into each other.

All triangulations are reachable via sequences of edge-flips: an elementary proof

A simple proof is provided for the fact that the set of all possible triangulations of a planar point set in a polygonal domain is closed under the basic diagonal flip operation.