Generating the 4-connected and strongly 4-connected triangulations on the torus and projective plane
The triangulations of the projective plane were shown by the author to be generated by the operation of vertex splitting from two minimal triangulations [``Generating the triangulations of the projective plane'', J. Comb. Theory, Ser. B 33, 222-230 (1982; Zbl 0509.52007)]. He shows here that if the same operation is applied to the same starting set of triangulations, but restricted so that vertices of degree 3 are never created, then the set of 4-connected triangulations of the projective plane is generated. With the additional restriction that two adjacent vertices of degree 4 are never created, the set of strongly 4-connected triangulations results. (A graph is strongly 4-connected if it is 4- connected and the removal of any 4-vertex-cut leaves a component which is a vertex.) The analogous statements are shown to be valid for the torus, with a starting set of 21 minimal triangulations.
scientific article; zbMATH DE number 4202275