Minimal quadrangulations of nonorientable surfaces (Q1116092)

A topological polyhedron on a compact 2-manifold is called a quadrangulation if each of its faces is a topological quadrangle (and if some obvious conditions avoid degenerations). Starting from the complete graph \(K_ n\) (n\(\equiv 1\) mod 4) and the general octahedral graph \(O_{2n}\) the authors construct minimal quadrangulations (i.e. with minimal number of quadrangles) of compact nonoriented surfaces, such that \(K_ n\) and \(O_{2n}\), resp., are their 1-skeletons. These results correspond to the classical triangulation-theorems by Ringel, Youngs and Jungerman.