Diagonal flips in triangulations of surfaces
A triangulation \(G\) of a closed surface \(\text{F}^ 2\) is a simple graph, without loops and multiple edges, which is embedded on \(\text{F}^ 3\) so that each face is triangular and so that any two faces meet along at most one edge. Let \(abc\) and \(acd\) be two triangular faces of \(G\) which have an edge \(ac\) in common. The diagonal flip of \(ac\) replaces the diagonal \(ac\) with \(bd\) in the quadrilateral \(abcd\). This note shows that for any closed surface \(\text{F}^ 2\), there exists a positive integer \(N\) such that two triangulations \(G\) and \(G'\) of \(\text{F}^ 2\) are equivalent to each other under diagonal flips if \(| V(G)|= | V(G')|\geq N\).
scientific article; zbMATH DE number 716459