Sander Verdonschot

We show that any triangulation on *n* vertices can be transformed into a
4-connected one using at most (3*n* - 6)/5 edge flips. We also give an
example of a triangulation that requires (3*n* - 10)/5 flips to be made
4-connected. Our result implies that any triangulation can be
transformed into any other by at most 5.2*n* - 24.4 flips.