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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 457–463 (Mi semr501)  
This article is cited in 3 scientific papers (total in 3 papers)

Discrete mathematics and mathematical cybernetics

The weight of edge in 3-polytopes

O. V. Borodina, A. O. Ivanovab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Ammosov North-Eastern Federal University, str. Kulakovskogo, 48, 677013, Yakutsk, Russia
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Abstract: The height of an edge in 3-polytopes is the maximum degree of its incident vertices and faces. In 1940, Lebesgue proved that each 3-polytope without pyramidal edges has an edge of height at most 11. This upper bound was lowered to 10 by Avgustinovich and Borodin (1995). The best known lower bound for the height of edges is 7.
We lower upper bound to 9 and give a construction of 3-polytope which has no edges of height smaller than 8.
Keywords: planar map, planar graph, 3-polytope, structural properties, height.
Received June 2, 2014, published June 16, 2014
Document Type: Article
UDC: 519.172.2
MSC: 05C15
Language: Russian
Citation: O. V. Borodin, A. O. Ivanova, “The weight of edge in 3-polytopes”, Sib. Èlektron. Mat. Izv., 11 (2014), 457–463
Citation in format AMSBIB
\Bibitem{BorIva14}
\by O.~V.~Borodin, A.~O.~Ivanova
\paper The weight of edge in 3-polytopes
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 457--463
\mathnet{http://mi.mathnet.ru/semr501}
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