Diagonal flips in triangulations on closed surfaces with minimum degree at least 4 (Q1305524)

Let \(abc\) and \(bad\) be two regions of an imbedded graph, sharing edge \(ab\). The diagonal flip of \(ab\) removes \(ab\) and then inserts \(cd\) in the quadrilateral region \(adbc\) just created. The authors show that any two triangulations of a closed surface of positive genus and having minimum degree at least 4 and the same order can be transformed into each other by a finite sequence of diagonal flips, if the order is large enough. The result extends to the sphere, if the join \(\overline K_2+ C_n\) is excluded.