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arXiv · 1110.6473

Making triangulations 4-connected using flips

Prosenjit Bose·Dana Jansens·André van Renssen·Maria Saumell·Sander Verdonschot
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Abstract

We show that any combinatorial triangulation on n vertices can be transformed into a 4-connected one using at most floor((3n - 9)/5) edge flips. We also give an example of an infinite family of triangulations that requires this many flips to be made 4-connected, showing that our bound is tight. In addition, for n >= 19, 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 - 33.6, improving on the previous best known bound of 6n - 30.

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Prosenjit Bose, Dana Jansens, André van Renssen, Maria Saumell, Sander Verdonschot. 2012-10-30. Making triangulations 4-connected using flips. https://doi.org/10.1016/j.comgeo.2012.10.012

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