Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on heterochromatic cycles of length 4 in edge-colored graphs   Let $G$ be an edge-colored graph. A heterochromatic cycle of $G$ is one in
which every two edges have different colors. For a vertex $v\in V(G)$, let
$CN(v)$ denote the set of colors which are assigned to the edges incident to
$v$. In this note we prove that $G$ contains a heterochromatic cycle of length
4 if $G$ has $n\geq 60$ vertices and $|CN(u)\cup CN(v)|\geq n-1$ for every pair
of vertices $u$ and $v$ of $G$. This extends a result of Broersma et al. on the
existence of heterochromatic cycles of length 3 or 4.

22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga