Autor: Nakamoto, Atsuhiro - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Flippable Edges in Triangulations on Surfaces
Autorzy:: Ikegami, Daiki
Nakamoto, Atsuhiro
Powiązania:: https://bibliotekanauki.pl/articles/32222665.pdf
Data publikacji:: 2022-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: triangulation
diagonal flip
surface
Opis:: Concerning diagonal flips on triangulations, Gao et al. showed that any triangulation G on the sphere with n ≥ 5 vertices has at least n − 2 flippable edges. Furthermore, if G has minimum degree at least 4 and n ≥ 9, then G has at least 2n + 3 flippable edges. In this paper, we give a simpler proof of their results, and extend them to the case of the projective plane, the torus and the Klein bottle. Finally, we give an estimation for the number of flippable edges of a triangulation on general surfaces, using the notion of irreducible triangulations.
Źródło:: Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1041-1059
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

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

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