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

We study the families of plane graphs determined by lower bounds ?$\delta$?, ?$\rho$?, ?$w$?, ?$w^\ast$? 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 ?$(2,\rho,w,w^\ast)$? 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). Obravnavamo družine ravninskih grafov določenih s spodnjimi mejami ?$\delta$?, ?$\rho$?, ?$w$?, ?$w^\ast$? za njihove vozliščne stopnje, velikosti lic, uteži povezav in uteži dualnih povezav. Nadaljujujoč prejšnjo raziskavo takšnih družin sestavljenih iz poliedrskih grafov določimo četverice ?$(2,\rho,w,w^\ast)$? za katere pridružena družina ni prazna. Poleg tega določimo vse četverice, ki imajo ekstremne družine (v tem smislu da s povečanjem katerekoli vrednosti četverice dobimo prazno družino).