Diagonal flips in triangulations of surfaces

Diagonal Flips of Triangulations on Surfaces , a Survey

Diagonal flips in pseudo-triangulations on closed surfaces

A pseudo-triangulation on a closed surface without loops is a graph embedded on the surface so that each face is triangular and may have multiple edges, but no lo $0$ps. We shall establish a theory of diagonal flips in those pseudotriangulations. Our theory will work in parallel to that for simple triangulations basically, but it will present more concrete theorems than the latter.

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.

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 Labelled Planar Triangulations

A classical result of Wagner states that any two (unlabelled) planar triangulations with the same number of vertices can be transformed into each other by a finite sequence of diagonal flips. Recently Komuro gives a linear bound on the maximum number of diagonal flips needed for such a transformation. In this paper we show that any two labelled triangulations can be transformed into each other ...