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Weight of faces in plane maps. (English. Russian original) Zbl 0958.52015
Math. Notes 64, No. 5, 562-570 (1998); translation from Mat. Zametki 64, No. 5, 648-657 (1998).
In his doctoral thesis (1994), O. V. Borodin described the structure of the neighbourhoods (in the combinatorial sense of weights) of edges and faces in several classes of planar graphs (with applications to problems of cyclic and simultaneous colorings). In particular, e.g. the edge neighbourhoods of 3-polytopes could be described in a detailed manner.
In the present paper, the authors investigate the structure of face neighbourhoods of planar graphs. More precisely, they derive exact upper bounds for the minimum weight of minor faces in normal planar maps and for 3-polytopes with specified maximal vertex degree.

MSC:
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
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