- Tytuł:
- Multicolor Ramsey numbers and star-critical Ramsey numbers involving fans
- Autorzy:
-
Li, Yan
Zhang, Yahui
Zhang, Ping - Tematy:
-
multicolor Ramsey number
star-critical Ramsey number
fan
book - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/59945814.pdf Link otwiera się w nowym oknie
- Opis:
- For graphs $G$ and $H$, the multicolor Ramsey number $r_{k+1}(G;H)$ is defined as the minimum integer $N$ such that any edge-coloring of $K_N$ by $k+1$ colors contains either a monochromatic $G$ in the first $k$ colors or a monochromatic $H$ in the last color. We shall write two color Ramsey numbers as $r(G,H)$. For graphs $F$, $G$ and $H$, let $F\to (G,H)$ signify that any red/blue edge coloring of $F$ contains either a red $G$ or a blue $H$. Define the star-critical Ramsey number $r^\ast(G,H)$ as $\max\{s | K_r\setminus K_{1,s}\to (G,H)\}$ where $r=R(G,H)$. A fan $F_n$ is a graph that consists of $n$ copies of $K_3$ sharing a common vertex, and a book $B_n^{(p)}$ is a graph that consists of $n$ copies of $K_{p+1}$ sharing a common $K_p$. In this note, we shall show the upper bounds for $r_{k+1}(K_{t,s};F_{n})$, $r_{k+1}(K_{2,s};F_{n})$, $r_{k+1}(C_{2t};F_{n})$, some of which are sharp up to the sub-linear term asymptotically. We also obtain the value of $r^\ast(F_m,B_n^{(p)})$ as $n\to\infty$.
- Dostawca treści:
- Biblioteka Nauki
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