Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Ramsey numbers of 3-uniform Berge cycles   For an arbitrary graph $G$, a hypergraph $\mathcal{H}$ is called Berge-$G$ if
there is a bijection $\Phi :E(G)\longrightarrow E( \mathcal{H})$ such that for
each $e\in E(G)$, we have $e\subseteq \Phi (e)$. We denote by $\mathcal{B}^rG$,
the family of $r$-uniform Berge-$G$ hypergraphs. For families $\mathcal{H}_1,
\mathcal{H}_2,\ldots, \mathcal{H}_t$ of $r$-uniform hypergraphs, the Ramsey
number $R(\mathcal{H}_1, \mathcal{H}_2,\ldots, \mathcal{H}_t)$ is the smallest
integer $n$ such that in every $t$-hyperedge coloring of $\mathcal{K}_{n}^r$
there is a monochromatic copy of a hypergraph in $\mathcal{H}_i$ of color $i$,
for some $1\leq i\leq t$.
  Recently, the Ramsey problems of Berge hypergraphs have been studied by many
researchers.
  In this paper, we focus on Ramsey number involving $3$-uniform Berge cycles
and we prove that for $n \geq 4$, $
R(\mathcal{B}^3C_n,\mathcal{B}^3C_n,\mathcal{B}^3C_3)=n+1.$ Moreover, for $m
\geq n\geq 6$ and $m\geq 11$, we show that
$R(\mathcal{B}^3K_m,\mathcal{B}^3C_n)= m+\lfloor \frac{n-1}{2}\rfloor -1.$ This
is the first result of Ramsey number for two different families of Berge
hypergraphs.

25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg