Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernelization and approximation of distance-$r$ independent sets on
  nowhere dense graphs   For a positive integer $r$, a distance-$r$ independent set in an undirected
graph $G$ is a set $I\subseteq V(G)$ of vertices pairwise at distance greater
than $r$, while a distance-$r$ dominating set is a set $D\subseteq V(G)$ such
that every vertex of the graph is within distance at most $r$ from a vertex
from $D$. We study the duality between the maximum size of a distance-$2r$
independent set and the minimum size of a distance-$r$ dominating set in
nowhere dense graph classes, as well as the kernelization complexity of the
distance-$r$ independent set problem on these graph classes. Specifically, we
prove that the distance-$r$ independent set problem admits an almost linear
kernel on every nowhere dense graph class.

5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th