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).
@article{1092,
title = {More on the structure of plane graphs with prescribed degrees of vertices, faces, edges and dual edges},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {14},
year = {2017},
doi = {10.26493/1855-3974.1092.e83},
language = {EN},
url = {http://dml.mathdoc.fr/item/1092}
}
Hudák, Peter; Maceková, Mária; Madaras, Tomáš; Široczki, Pavol. More on the structure of plane graphs with prescribed degrees of vertices, faces, edges and dual edges. ARS MATHEMATICA CONTEMPORANEA, Tome 14 (2017) . doi : 10.26493/1855-3974.1092.e83. http://gdmltest.u-ga.fr/item/1092/