论文标题
多部分ramsey编号$ m_j（k_m，nk_2）$
Multipartite Ramsey number $m_j(K_m, nK_2)$
论文作者
论文摘要
假设$ k_ {j \ times n} $是一个完整的多部分图，由$ j $ partite集和每个零件集中的$ n $顶点组成。对于给定的图，$ g_1，g_2，\ ldots，g_n $，多部分ramsey号码（m-r-number）$ m_j（g_1，g_1，g_2，\ ldots，g_n）$是最小的整数$ t $，因此对于任何$ n $ n $ n $ n $ n $ n $ n $ n $ - ge^^1，g^^1，g^1，g^2，\ ldots y ed ed ed ed ed ed y g^n $ $ k_ {j \ times t} $，$ g^i $包含至少一个$ i $的$ g_i $的单色副本。 $ j，n \ geq 2 $和$ 4 \ leq m \ leq m \ leq 6 $，m-r-number $ m_j（nk_2，c_7）$的大小，$ j，n \ geq 2 $和$ 4 \ geq 2 $和$ 4 $j,n\geq 2$, the size of M-R-number $m_j(K_3,K_3, n_1K_2,n_2K_,\ldots,n_iK_2)$ for $j \leq 6$ and $i,n_i\geq 1$ and the size of M-R-number $m_j(K_3,K_3, nK_2)$ for $j \geq 2$到目前为止，已经在几篇论文中计算出$ n \ geq 1 $。在本文中，我们获得了M-R-number $ M_J（k_m，nk_2）$的值，每个$ j，n \ geq 2 $和每个$ m \ geq 4 $。
Assume that $K_{j\times n}$ be a complete, multipartite graph consisting of $j$ partite sets and $n$ vertices in each partite set. For given graphs $G_1, G_2,\ldots, G_n$, the multipartite Ramsey number (M-R-number) $m_j(G_1, G_2, \ldots,G_n)$ is the smallest integer $t$ such that for any $n$-edge-coloring $(G^1,G^2,\ldots, G^n)$ of the edges of $K_{j\times t}$, $G^i$ contains a monochromatic copy of $G_i$ for at least one $i$. The size of M-R-number $m_j(nK_2, C_m)$ for $j, n\geq 2$ and $4\leq m\leq 6$, the size of M-R-number $m_j(nK_2, C_7)$ for $j \geq 2$ and $n\geq 2$, the size of M-R-number $m_j(nK_2,K_3)$, for each $j,n\geq 2$, the size of M-R-number $m_j(K_3,K_3, n_1K_2,n_2K_,\ldots,n_iK_2)$ for $j \leq 6$ and $i,n_i\geq 1$ and the size of M-R-number $m_j(K_3,K_3, nK_2)$ for $j \geq 2$ and $n\geq 1$ have been computed in several papers up to now. In this article we obtain the values of M-R-number $m_j(K_m, nK_2)$, for each $j,n\geq 2$ and each $m\geq 4$.
