Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new upper bound on the acyclic chromatic indices of planar graphs   An acyclic edge coloring of a graph $G$ is a proper edge coloring such that
no bichromatic cycles are produced. The acyclic chromatic index $a'(G)$ of $G$
is the smallest integer $k$ such that $G$ has an acyclic edge coloring using
$k$ colors. It was conjectured that $a'(G)\le \Delta+2$ for any simple graph
$G$ with maximum degree $\Delta$. In this paper, we prove that if $G$ is a
planar graph, then $a'(G)\leq\Delta +7$. This improves a result by Basavaraju
et al. [{\em Acyclic edge-coloring of planar graphs}, SIAM J. Discrete Math.,
25 (2011), pp. 463-478], which says that every planar graph $G$ satisfies
$a'(G)\leq\Delta +12$.

23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol