Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Star-critical Ramsey number of $K_4$ versus $F_n$   For two graphs $G$ and $H$, the Ramsey number $r(G,H)$ is the smallest
positive integer $r$, such that any red/blue coloring of the edges of the graph
$K_r$ contains either a red subgraph that is isomorphic to $G$ or a blue
subgraph that is isomorphic to $H$. Let $S_k=K_{1,k}$ be a star of order $k+1$
and $K_n\sqcup S_k$ be a graph obtained from $K_n$ by adding a new vertex $v$
and joining $v$ to $k$ vertices of $K_n$. The star-critical Ramsey number
$r_*(G,H)$ is the smallest positive integer $k$ such that any red/blue coloring
of the edges of graph $K_{r-1}\sqcup S_k$ contains either a red subgraph that
is isomorphic to $G$ or a blue subgraph that is isomorphic to $H$, where
$r=r(G,H)$. In this paper, it is shown that $r_*(F_n,K_4)=4n+2$, where
$n\geq{4}$.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg