Edge‐maximal graphs on orientable and some nonorientable surfaces
James Davies, Florian Pfender · Journal of Graph Theory · 2021
Abstract We study edge‐maximal, noncomplete graphs on surfaces that do not triangulate the surface. We prove that there is no such graph on the projective plane is the unique such graph on the Klein bottle and is the unique such graph on the torus . In contrast to this for each we construct an infinite family of such graphs on the orientable surface of genus , that are edges short of a triangulation.