论文标题
漫长周期和完整图的拉姆齐号
The Ramsey number of a long cycle and complete graphs
论文作者
论文摘要
In this paper, we prove that the multicolored Ramsey number $R(G_1,\dots,G_n,K_{n_1},\dots,K_{n_r})$ is at least $(γ-1)(κ-1)+1$ for arbitrary connected graphs $G_1,\dots,G_n$ and $ n_1，\ dots，n_r \ in \ mathbb {n} $，其中$γ= r（g_1，\ dots，g_n）$和$κ= r（k_ {n_1}，\ dots，\ dots，k_ {n_r}）$。 Al的Erd \ H OS。推测$ r（c_n，k_l）=（n-1）（l-1）（l-1）+1 $每$ n \ geq l \ geq 3 $，除了$ n = l = 3 $外。 Nikiforov证明了$ N \ GEQ 4L+2 $的猜想。使用上面的结合，我们得出了此结果的以下概括。 $ r（c_n，k_ {n_1}，\ dots，k_ {n_r}）=（n-1）（κ-1）+1 $，其中$κ= r（k_ {n_1}，\ dots，k_ {n_r}）$和$ n \ geq4κ+2 $。
In this paper, we prove that the multicolored Ramsey number $R(G_1,\dots,G_n,K_{n_1},\dots,K_{n_r})$ is at least $(γ-1)(κ-1)+1$ for arbitrary connected graphs $G_1,\dots,G_n$ and $n_1,\dots,n_r\in\mathbb{N}$, where $γ=R(G_1,\dots,G_n)$ and $κ=R(K_{n_1},\dots,K_{n_r})$. Erd\H os at al. conjectured that $R(C_n,K_l)=(n-1)(l-1)+1$ for every $n\geq l\geq 3$ except for $n=l=3$. Nikiforov proved this conjecture for $n\geq 4l+2$. Using the above bound, we derive the following generalization of this result. $R(C_n,K_{n_1},\dots,K_{n_r})=(n-1)(κ-1)+1$, where $κ=R(K_{n_1},\dots,K_{n_r})$ and $n\geq 4κ+2$.
