Geodesic
More on the structure of plane graphs with prescribed degrees of vertices, faces, edges and dual edges
Ars Mathematica Contemporanea, Tome 13 (2017) no. 2, pp. 355-366.

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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).
DOI : 10.26493/1855-3974.1092.e83
Keywords: Plane graph, girth, edge weight, dual edge weight 
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Peter Hudák; Mária Maceková; Tomáš Madaras; Pavol Široczki. More on the structure of plane graphs with prescribed degrees of vertices, faces, edges and dual edges. Ars Mathematica Contemporanea, Tome 13 (2017) no. 2, pp. 355-366. doi : 10.26493/1855-3974.1092.e83. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1092.e83/

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