Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A solution to a conjecture on the rainbow connection number   For a graph $G$, Chartrand et al. defined the rainbow connection number
$rc(G)$ and the strong rainbow connection number $src(G)$ in "G. Charand, G.L.
John, K.A. Mckeon, P. Zhang, Rainbow connection in graphs, Mathematica
Bohemica, 133(1)(2008) 85-98". They raised the following conjecture: for two
given positive $a$ and $b$, there exists a connected graph $G$ such that
$rc(G)=a$ and $src(G)=b$ if and only if $a=b\in\{1,2\}$ or $ 3\leq a\leq b$".
In this short note, we will show that the conjecture is true.

10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph