Diagonal flips in pseudo-triangulations on closed surfaces Original Research Article

Negami has already shown that there is a natural number N(F2) for any closed surface F2 such that two triangulations on F2 with n vertices can be transformed into each other by a sequence of diagonal flips if n⩾N(F2). We investigate the same theorem for pseudo-triangulations with or without loops, estimating the length of a sequence of diagonal flips. Our arguments will be applied to simple triangulations to obtain a linear upper bound for N(F2) with respect to the genus of F2.