Making triangulations 4-connected using flips

Details Making triangulations 4-connected using flips Making triangulations 4-connected using flips

2011-10-28

arxiv.org/abs/1110.6473v1

Computer Science

Computational Geometry

20 pages, 8 figures. Submitted to CGTA special issue for CCCG 2011. Conference version available at http://2011.cccg.ca/PDFs

Scientific paper

We show that any triangulation on n vertices can be transformed into a 4-connected one using at most floor((3n - 7)/5) edge flips. We also give an example of a triangulation that requires ceil((3n - 10)/5) flips to be made 4-connected, showing that our bound is tight. In addition, we improve the upper bound on the number of flips required to transform any 4-connected triangulation into the canonical triangulation (the triangulation with two dominant vertices), matching the known lower bound of 2n - 15. Our results imply a new upper bound on the diameter of the flip graph of 5.2n - 32.8, improving on the previous best known bound of 6n - 30.

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