Describing Neighborhoods of 5-Vertices in a Class of 3-Polytopes with Minimum Degree 5
- 作者: Borodin O.1, Ivanova A.1, Nikiforov D.1
-
隶属关系:
- Sobolev Institute of Mathematics
- 期: 卷 59, 编号 1 (2018)
- 页面: 43-49
- 栏目: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171644
- DOI: https://doi.org/10.1134/S0037446618010056
- ID: 171644
如何引用文章
详细
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.
作者简介
O. Borodin
Sobolev Institute of Mathematics
编辑信件的主要联系方式.
Email: brdnoleg@math.nsc.ru
俄罗斯联邦, Novosibirsk
A. Ivanova
Sobolev Institute of Mathematics
Email: brdnoleg@math.nsc.ru
俄罗斯联邦, Novosibirsk
D. Nikiforov
Sobolev Institute of Mathematics
Email: brdnoleg@math.nsc.ru
俄罗斯联邦, Novosibirsk