- Tytuł:
- On the Restricted Size Ramsey Number Involving a Path P3
- Autorzy:
-
Silaban, Denny Riama
Baskoro, Edy Tri
Uttunggadewa, Saladin - Powiązania:
- https://bibliotekanauki.pl/articles/31343288.pdf
- Data publikacji:
- 2019-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
restricted size Ramsey number
path
connected graph
star - Opis:
- For any pair of graphs $G$ and $H$, both the size Ramsey number $ \hat{r}(G,H) $ and the restricted size Ramsey number $ r^\ast (G,H) $ are bounded above by the size of the complete graph with order equals to the Ramsey number $ r(G,H) $, and bounded below by $ e(G) + e(H) − 1 $. Moreover, trivially,$ \hat{r} (G,H) \le r^\ast (G,H) $. When introducing the size Ramsey number for graph, Erdős et al. (1978) asked two questions; (1) Do there exist graphs $G$ and $H$ such that $ \hat{r} (G,H) $ attains the upper bound? and (2) Do there exist graphs $G$ and $H$ such that $ \hat{r} (G,H) $ is significantly less than the upper bound? In this paper we consider the restricted size Ramsey number $ r^\ast (G,H) $. We answer both questions above for $ r^\ast (G,H) $ when $ G = P_3 $ and $H$ is a connected graph.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2019, 39, 3; 757-769
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł