Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramsey and Gallai-Ramsey numbers for two classes of unicyclic graphs   Given a graph $G$ and a positive integer $k$, define the \emph{Gallai-Ramsey
number} to be the minimum number of vertices $n$ such that any $k$-edge
coloring of $K_n$ contains either a rainbow (all different colored) triangle or
a monochromatic copy of $G$. In this paper, we consider two classes of
unicyclic graphs, the star with an extra edge and the path with a triangle at
one end. We provide the $2$-color Ramsey numbers for these two classes of
graphs and use these to obtain general upper and lower bounds on the
Gallai-Ramsey numbers.

31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th