More on the structure of plane graphs with prescribed degrees of vertices, faces, edges and dual edges

Abstract

We study the families of plane graphs determined by lower bounds δ, ρ, w, w^* on their vertex degrees, face sizes, edge weights and dual edge weights, respectively. Continuing the previous research of such families comprised of polyhedral graphs, we determine the quadruples (2, ρ, w, w^*) for which the associated family is non-empty. In addition, we determine all quadruples which yield extremal families (in the sense that the increase of any value of a quadruple results in an empty family).