Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partitioning sparse graphs into an independent set and a forest of
  bounded degree   An $({\cal I},{\cal F}_d)$-partition of a graph is a partition of the
vertices of the graph into two sets $I$ and $F$, such that $I$ is an
independent set and $F$ induces a forest of maximum degree at most $d$. We show
that for all $M<3$ and $d \ge \frac{2}{3-M} - 2$, if a graph has maximum
average degree less than $M$, then it has an $({\cal I},{\cal F}_d)$-partition.
Additionally, we prove that for all $\frac{8}{3} \le M < 3$ and $d \ge
\frac{1}{3-M}$, if a graph has maximum average degree less than $M$ then it has
an $({\cal I},{\cal F}_d)$-partition.

27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics