Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the edge partition of graphs containing either a light edge or
  an alternating 2-cycle   Let $\mathcal{G}_{\alpha}$ be a hereditary graph class (i.e, every subgraph
of $G_{\alpha}\in \mathcal{G}_{\alpha}$ belongs to $\mathcal{G}_{\alpha}$) such
that every graph $G_{\alpha}$ in $\mathcal{G}_{\alpha}$ has minimum degree at
most 1, or contains either an edge $uv$ such that
$d_{G_{\alpha}}(u)+d_{G_{\alpha}}(v)\leq \alpha$ or a 2-alternating cycle. It
is proved that every graph in $\mathcal{G}_{\alpha}$ ($\alpha\geq 5$) with
maximum degree $\Delta$ can be edge-partitioned into two forests $F_1$, $F_2$
and a subgraph $H$ such that $\Delta(F_i)\leq
\max\{2,\lceil\frac{\Delta-\alpha+6}{2}\rceil\}$ for $i=1,2$ and $\Delta(H)\leq
\alpha-5$.

16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph