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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).

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