2011/10/31 by Prosenjit Bose, Dana Jansens, André van Renssen +2 · 1 citation
Computer Science · #cs.CG
paper · pdf · doi:10.1016/j.comgeo.2012.10.012
published as Computational Geometry: Theory and Applications, 47(2A):187-197, 2014. Special issue for CCCG 2011 · 22 pages, 8 figures. Accepted to CGTA special issue for CCCG 2011. Conference version available at http://2011.cccg.ca/PDFschedule/papers/paper34.pdf
arxiv created 2012/10/30 · arxiv updated 2015/09/09
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.