Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Edge-colorings of $K_{m,n}$ which Forbid Multicolored Cycles   A subgraph in an edge-colored graph is multicolored if all its edges receive
distinct colors. In this paper, we study the proper edge-colorings of the
complete bipartite graph $K_{m,n}$ which forbid multicolored cycles. Mainly, we
prove that (1) for any integer $k\geq 2$, if $n\geq 5k-6$, then any properly
$n$-edge-colored $K_{k,n}$ contains a multicolored $C_{2k}$, and (2) determine
the order of the properly edge-colored complete bipartite graphs which forbid
multicolored $C_6$.

32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol