Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anti-Ramsey number of edge-disjoint rainbow spanning trees   An edge-colored graph $G$ is called rainbow if every edge of $G$ receives a
different color. The anti-Ramsey number of $t$ edge-disjoint rainbow spanning
trees, denoted by $r(n,t)$, is defined as the maximum number of colors in an
edge-coloring of $K_n$ containing no $t$ edge-disjoint rainbow spanning trees.
Jahanbekam and West [J. Graph Theory, 2014] conjectured that for any fixed $t$,
$r(n,t)=\binom{n-2}{2}+t$ whenever $n\geq 2t+2 \geq 6$. In this paper, we prove
this conjecture. We also determine $r(n,t)$ when $n = 2t+1$. Together with
previous results, this gives the anti-Ramsey number of $t$ edge-disjoint
rainbow spanning trees for all values of $n$ and $t$.

10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int