Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On incidence coloring conjecture in Cartesian products of graphs   An incidence in a graph $G$ is a pair $(v,e)$ where $v$ is a vertex of $G$
and $e$ is an edge of $G$ incident to $v$. Two incidences $(v,e)$ and $(u,f)$
are adjacent if at least one of the following holds: $(a)$ $v = u$, $(b)$ $e =
f$, or $(c)$ $vu \in \{e,f\}$. An incidence coloring of $G$ is a coloring of
its incidences assigning distinct colors to adjacent incidences. It was
conjectured that at most $\Delta(G) + 2$ colors are needed for an incidence
coloring of any graph $G$. The conjecture is false in general, but the bound
holds for many classes of graphs. We introduce some sufficient properties of
the two factor graphs of a Cartesian product graph $G$ for which $G$ admits an
incidence coloring with at most $\Delta(G) + 2$ colors.

28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th