Describing Neighborhoods of 5-Vertices in a Class of 3-Polytopes with Minimum Degree 5
- Autores: Borodin O.1, Ivanova A.1, Nikiforov D.1
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Afiliações:
- Sobolev Institute of Mathematics
- Edição: Volume 59, Nº 1 (2018)
- Páginas: 43-49
- Seção: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171644
- DOI: https://doi.org/10.1134/S0037446618010056
- ID: 171644
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Resumo
Lebesgue proved in 1940 that each 3-polytope with minimum degree 5 contains a 5-vertex for which the set of degrees of its neighbors is majorized by one of the following sequences
(6, 6, 7, 7, 7), (6, 6, 6, 7, 9), (6, 6, 6, 6, 11)
(5, 6, 7, 7, 8), (5, 6, 6, 7, 12), (5, 6, 6, 8, 10), (5, 6, 6, 6, 17)
(5, 5, 7, 7, 13), (5, 5, 7, 8, 10), (5, 5, 6, 7, 27), (5, 5, 6, 6,∞), (5, 5, 6, 8, 15), (5, 5, 6, 9, 11)
(5, 5, 5, 7, 41), (5, 5, 5, 8, 23), (5, 5, 5, 9, 17), (5, 5, 5, 10, 14), (5, 5, 5, 11, 13).
We prove that each 3-polytope with minimum degree 5 without vertices of degree from 7 to 10 contains a 5-vertex whose set of degrees of its neighbors is majorized by one of the following sequences: (5, 6, 6, 5, ∞), (5, 6, 6, 6, 15), and (6, 6, 6, 6, 6), where all parameters are tight.
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Sobre autores
O. Borodin
Sobolev Institute of Mathematics
Autor responsável pela correspondência
Email: brdnoleg@math.nsc.ru
Rússia, Novosibirsk
A. Ivanova
Sobolev Institute of Mathematics
Email: brdnoleg@math.nsc.ru
Rússia, Novosibirsk
D. Nikiforov
Sobolev Institute of Mathematics
Email: brdnoleg@math.nsc.ru
Rússia, Novosibirsk
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