## Abstract Simultaneous diagonal flips in plane triangulations are investigated. It is proved that every triangulation with __n__ββ₯β6 vertices has a simultaneous flip into a 4βconnected triangulation, and that the set of edges to be flipped can be computed in $\cal O$(__n__) time. It follows that
Diagonal flips in triangulations of surfaces
β Scribed by Seiya Negami
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 518 KB
- Volume
- 135
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
Consider a class P of triangulations on a closed surface F 2 , closed under vertex splitting. We shall show that any two triangulations with the same and sufficiently large number of vertices which belong to P can be transformed into each other, up to homeomorphism, by a finite sequence of diagonal
It will be shown that any two triangulations on a closed surface, except the sphere, with minimum degree at least 4 can be transformed into each other by a finite sequence of diagonal flips through those triangulations if they have a sufficiently large and same number of vertices. The same fact hold
We use the generating function approach to enumerate two families of rooted planar near-triangulations (2-connected, and 2-connected with no multiple edges) with respect to the number of flippable edges. It is shown that their generating functions are algebraic. Simple explicit expressions are obtai
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## Abstract The vertices of each plane triangulation without loops and multiple edges may be colored with 11 colors so that for every two adjacent triangles [__xyz__] and [__wxy__], the vertices __x__,__y__,__w__,__z__ are colored pairwise differently.