- Tytuł:
- On the Weight of Minor Faces in Triangle-Free 3-Polytopes
- Autorzy:
-
Borodin, Oleg V.
Ivanova, Anna O. - Powiązania:
- https://bibliotekanauki.pl/articles/31340872.pdf
- Data publikacji:
- 2016-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
plane map
plane graph
3-polytope
structural property
weight of face - Opis:
- The weight w(f) of a face f in a 3-polytope is the degree-sum of vertices incident with f. It follows from Lebesgue’s results of 1940 that every triangle-free 3-polytope without 4-faces incident with at least three 3-vertices has a 4-face with w ≤ 21 or a 5-face with w ≤ 17. Here, the bound 17 is sharp, but it was still unknown whether 21 is sharp. The purpose of this paper is to improve this 21 to 20, which is best possible.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 603-619
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł