- Tytuł:
- Describing Neighborhoods of 5-Vertices in 3-Polytopes with Minimum Degree 5 and Without Vertices of Degrees from 7 to 11
- Autorzy:
-
Borodin, Oleg V.
Ivanova, Anna O.
Kazak, Olesya N. - Powiązania:
- https://bibliotekanauki.pl/articles/31342287.pdf
- Data publikacji:
- 2018-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
planar graph
structure properties
3-polytope
neighborhood - Opis:
- In 1940, Lebesgue proved that every 3-polytope 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). In this paper we prove that every 3-polytope without vertices of degree from 7 to 11 contains a 5-vertex for which the set of degrees of its neighbors is majorized by one of the following sequences: (5, 5, 6, 6, ∞), (5, 6, 6, 6, 15), (6, 6, 6, 6, 6), where all parameters are tight.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2018, 38, 3; 615-625
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł