- Tytuł:
- Light Minor 5-Stars in 3-Polytopes with Minimum Degree 5 and No 6-Vertices
- Autorzy:
-
Borodin, Oleg V.
Ivanova, Anna O.
Vasil’eva, Ekaterina I. - Powiązania:
- https://bibliotekanauki.pl/articles/31348169.pdf
- Data publikacji:
- 2020-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
planar map
planar graph
3-polytope
structural properties
5-star
weight
height - Opis:
- In 1940, Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class P5 of 3-polytopes with minimum degree 5. Given a 3-polytope P, by w(P) denote the minimum of the degree-sum (weight) of the neighborhoods of 5-vertices (minor 5-stars) in P. In 1996, Jendrol’ and Madaras showed that if a polytope P in P5 is allowed to have a 5-vertex adjacent to four 5-vertices, then w(P) can be arbitrarily large. For each P in P5 without vertices of degree 6 and 5-vertices adjacent to four 5-vertices, it follows from Lebesgue’s Theorem that w(P) ≤ 68. Recently, this bound was lowered to w(P) ≤ 55 by Borodin, Ivanova, and Jensen and then to w(P) ≤ 51 by Borodin and Ivanova. In this note, we prove that every such polytope P satisfies w(P) ≤ 44, which bound is sharp.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 985-994
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł