GENERATING THE 4-CONNECTED AND STRONGLY 4-CONNECTED TRIANGULATIONS ON THE TORUS AND PROJECTIVE PLANE

The triangulations of the torus can be generated from a set of 21 minimal triangulations by vertex splitting. We show that if we never create a 3-valent vertex when we split them we generate the 4-connected triangulations. In addition if we never create two adjacent 4-valent vertexes then we generate the strongly 4-connected triangulations. © 1990.