Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Another view of Bipartite Ramsey numbers   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
$m\geq 1$.

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The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph