Abstract
Negami has already shown that there is a natural number N(F 2) for any closed surface F 2 such that two triangulations on F 2 with n vertices can be transformed into each other by a sequence of diagonal flips if n⩾N(F 2) . 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(F 2) with respect to the genus of F 2 .
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