Weight of faces in plane maps
type: Item
instance of: scholarly article
title: Weight of faces in plane maps
zbMATH Open document ID: 0958.52015
DOI: 10.1007/BF02316280
author: Oleg V. Borodin
author: Douglas R. Woodall
published in: Mathematical Notes
publication date: 2001-04-16T00:00:00Z
review text: 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.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52B05
zbMATH DE Number: 1407574
zbMATH Keywords: polytope graphs
zbMATH Keywords: Steinitz theorem
zbMATH Keywords: normal planar map
zbMATH Keywords: face degree
zbMATH Keywords: planar graphs
zbMATH Keywords: 3-polytopes
zbMATH Keywords: vertex degree
MaRDI profile type: Publication
cites work: Quelques consequences simples de la formule d'Euler
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cites work: Q4005019
cites work: Triangulated \(3\)-polytopes without faces of low weight
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cites work: Cyclic degrees of 3-polytopes
full work available at URL: https://doi.org/10.1007/bf02316280
OpenAlex ID: W1992955076
description: scientific article; zbMATH DE number 1407574