More on the structure of plane graphs with prescribed degrees of vertices, faces, edges and dual edges - Hudák, Peter (Ars mathematica contemporanea, 2017)
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).
Keywords: ožina; ravninski graf; utež dualne povezave; utež povezave