\documentclass[12pt]{article}
\usepackage{amsmath,mathrsfs,bbm}
\usepackage{amssymb}
\textwidth=4.825in
\overfullrule=0pt
\thispagestyle{empty}

\begin{document}
\noindent
%
%
{\bf Zhang Rui and Sun Yongqi}
%
%

\medskip
\noindent
%
%
{\bf The Bipartite Ramsey Numbers $b(C_{2m};K_{2,2})$}
%
%

\vskip 5mm
\noindent
%
%
%
%
Given bipartite graphs $H_1$ and $H_2$, the bipartite Ramsey number
$b(H_1; H_2)$ is the smallest integer $b$ such that any subgraph $G$
of the complete bipartite graph $K_{b,b}$, either $G$ contains a copy
of $H_1$ or its complement relative to $K_{b,b}$ contains a copy of
$H_2$. It is known that $b(K_{2,2};K_{2,2})=5, b(K_{2,3};K_{2,3})=9,
b(K_{2,4};K_{2,4})=14$ and $b(K_{3,3};K_{3,3})=17$. In this paper we
study the case $H_1$ being even cycles and $H_2$ being $K_{2,2}$,
prove that $b(C_6;K_{2,2})=5$ and $b(C_{2m};K_{2,2})=m+1$ for $m\geq
4$.

\end{document}

.
