论文标题
$ M $ -Bipittite Ramsey编号$ BR_M（k_ {2,2}，k_ {5,5}）$
The $m$-bipartite Ramsey number $BR_m(K_{2,2},K_{5,5})$
论文作者
论文摘要
The bipartite Ramsey number $BR(H_1,H_2,\ldots,H_k)$, is the smallest positive integer $b$, such that each $k$-decomposition of $E(K_{b,b})$ contains $H_i$ in the $i$-th class for some $i, 1\leq i\leq k$.作为两部分Ramsey数字的另一视图，给定两个两部分图$ h_1 $和$ h_2 $以及一个正整数$ m $，$ m $ -bipartite ramsey number $ br_m（h_1，h_2）$，定义为最少的整数$ n $，以至于$ k_ n $ n $ k__ n $ n} $ h_1 \ subseteq h $或$ h_2 \ subseteq \ overline {h} $。 $ br_m（k_ {2,2}，k_ {3,3}）$，$ br_m（k_ {2,2}，k_ {2,2}，k_ {4,4}）$ for $ m $ $ m $，$ br_m（k_ {3,3}，k_ {3,3}，k_ {3,3,3}）的大小已确定为$ M $ M M，现在已经确定了几个$ M的$ M。另外，显示出$ br（k_ {2,2}，k_ {5,5}）= 17 $。在本文中，我们计算了$ br_m（k_ {2,2}，k_ {5,5}）$的$ m \ geq 2 $。
The bipartite Ramsey number $BR(H_1,H_2,\ldots,H_k)$, is the smallest positive integer $b$, such that each $k$-decomposition of $E(K_{b,b})$ contains $H_i$ in the $i$-th class for some $i, 1\leq i\leq k$. As another view of bipartite Ramsey numbers, for given two bipartite graphs $H_1$ and $H_2$ and a positive integer $m$, the $m$-bipartite Ramsey number $BR_m(H_1, H_2)$, is defined as the least integer $n$, such that any subgraph of $K_{m,n}$ say $H$, results in $H_1\subseteq H$ or $H_2\subseteq \overline{H}$. The size of $BR_m(K_{2,2}, K_{3,3})$, $BR_m(K_{2,2}, K_{4,4})$ for each $m$, and the size of $BR_m(K_{3,3}, K_{3,3})$ for some $m$, have been determined in several papers up to now. Also, it is shown that $BR(K_{2,2}, K_{5,5})=17$. In this article, we compute the size of $BR_m(K_{2,2}, K_{5,5})$ for some $m\geq 2$.
