Generating triangulations on closed surfaces with minimum degree at least 4 (Q1349104)

The authors show that every triangulation of a closed surface \(S\), other than the sphere, having minimum degree at least 4 can be obtained from an irreducible triangulation of \(S\) by two types of local deformation: (1) ``splitting'' a vertex into two adjacent vertices of degree at least 4 (reversing an edge contraction) and (2) ``adding an octahedron'' by completing the graph \(K_{2,2,2}\) within a given triangle. They also show that every triangulation of the sphere having minimum degree at least 4 can be obtained from \(K_{2,2,2}\) by using (1) and (2).