A generating theorem of punctured surface triangulations with inner degree at least 4

Given any punctured surface F2, we present a method for generating all of F2 triangulations with inner vertices of degree ≥ 4 and boundary vertices of degree ≥ 3. The method is based on a set of expansive operations which includes the well-known vertex splitting and octahedron addition. By reversing this method we get a procedure to obtain minimal triangulations by a sequence of intermediate triangulations, all of them within the given family.