Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong edge-colorings of sparse graphs with large maximum degree   A {\em strong $k$-edge-coloring} of a graph $G$ is a mapping from $E(G)$ to
$\{1,2,\ldots,k\}$ such that every two adjacent edges or two edges adjacent to
the same edge receive distinct colors. The {\em strong chromatic index}
$\chi_s'(G)$ of a graph $G$ is the smallest integer $k$ such that $G$ admits a
strong $k$-edge-coloring. We give bounds on $\chi_s'(G)$ in terms of the
maximum degree $\Delta(G)$ of a graph $G$. when $G$ is sparse, namely, when $G$
is $2$-degenerate or when the maximum average degree ${\rm Mad}(G)$ is small.
We prove that the strong chromatic index of each $2$-degenerate graph $G$ is at
most $5\Delta(G) +1$. Furthermore, we show that for a graph $G$, if ${\rm
Mad}(G)< 8/3$ and $\Delta(G)\geq 9$, then $\chi_s'(G)\leq 3\Delta(G) -3$ (the
bound $3\Delta(G) -3$ is sharp) and if ${\rm Mad}(G)<3$ and $\Delta(G)\geq 7$,
then $\chi_s'(G)\leq 3\Delta(G)$ (the restriction ${\rm Mad}(G)<3$ is sharp).

23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph