- Tytuł:
- Looseness and Independence Number of Triangulations on Closed Surfaces
- Autorzy:
-
Nakamoto, Atsuhiro
Negami, Seiya
Ohba, Kyoji
Suzuki, Yusuke - Powiązania:
- https://bibliotekanauki.pl/articles/31340887.pdf
- Data publikacji:
- 2016-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
triangulations
closed surfaces
looseness
k-loosely tight
independence number - Opis:
- The looseness of a triangulation $G$ on a closed surface $ F^2$, denoted by $ \xi (G) $, is defined as the minimum number $k$ such that for any surjection $ c : V (G) \rightarrow {1, 2, . . ., k + 3} $, there is a face $uvw$ of $G$ with $c(u)$, $c(v)$ and $c(w)$ all distinct. We shall bound $ \xi (G) $ for triangulations $G$ on closed surfaces by the independence number of $G$ denoted by $ \alpha(G) $. In particular, for a triangulation $G$ on the sphere, we have $ \xi (G) \le \frac{11 \alpha (G) - 10}{6} $ and this bound is sharp. For a triangulation $G$ on a non-spherical surface $F^2$, we have $ \xi (G) \le 2 \alpha (G) + \mathcal{l}(F^2) − 2 $, where $ \mathcal{l}(F^2) = \floor{ (2 − \chi (F^2))//2 } $ with Euler characteristic $ \chi (F^2) $.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 545-554
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł