Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partitioning 3-edge-colored complete equi-bipartite graphs by
  monochromatic trees under a color degree condition   The monochromatic tree partition number of an $r$-edge-colored graph $G$,
denoted by $t_r(G)$, is the minimum integer $k$ such that whenever the edges of
$G$ are colored with $r$ colors, the vertices of $G$ can be covered by at most
$k$ vertex-disjoint monochromatic trees. In general, to determine this number
is very difficult. For 2-edge-colored complete multipartite graph, Kaneko,
Kano, and Suzuki gave the exact value of $t_2(K(n_1,n_2,...,n_k))$. In this
paper, we prove that if $n\geq 3$, and K(n,n) is 3-edge-colored such that every
vertex has color degree 3, then $t_3(K(n,n))=3.$

30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs