论文标题
二手拉姆西数字的另一个观点
Another view of Bipartite Ramsey numbers
论文作者
论文摘要
对于两部分图形，$ g $和$ h $以及一个正整数$ m $，$ m $ -bipartite ramsey number $ br_m（g，h）$ g $和$ g $和$ h $是最小的整数$ n $，因此每种$ k_ {m，n} $ resuffe y y read $ k_ {m，n} $ resuft in Red $ g $ g $ g $ g $ $ g $或a Blue g $ $ h $。 \ cite {bi2018another}的Zhenming Bi，Gary Chartrand和Ping Zhang评估所有积极整数$ m $时，当$ g = k = k_ {2,2,2} $和$ h \ in \ in \ in \ {k_ {2,3}，k_ {2,3}，k_ {3,3,3} $ br_5（k_ {2,2}，k_ {3,3}）= br_6（k_ {2,2}，k_ {3,3}）= 12 $和$ br_7（k_ {2,2}，k_ {2,2}，k_ {3,3}在本文中，通过简短而简单的参数，我们确定每个$ M \ geq 1 $的$ br_m（k_ {2,2}，k_ {3,3}）$的确切值。
For bipartite graphs $G$ and $H$ and a positive integer $m$, the $m$-bipartite Ramsey number $BR_m(G, H)$ of $G$ and $H$ is the smallest integer $n$, such that every red-blue coloring of $K_{m,n}$ results in a red $G$ or a blue $H$. Zhenming Bi, Gary Chartrand and Ping Zhang in \cite{bi2018another} evaluate this numbers for all positive integers $m$ when $G= K_{2,2}$ and $H \in \{K_{2,3}, K_{3,3}\}$, especially in a long and hard argument they showed that $BR_5(K_{2,2}, K_{3,3}) = BR_6(K_{2,2}, K_{3,3}) = 12$ and $BR_7(K_{2,2}, K_{3,3}) = BR_8(K_{2,2}, K_{3,3}) = 9$. In this article, by a short and easy argument we determine the exact value of $BR_m(K_{2,2}, K_{3,3})$ for each $m\geq 1$.
