Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Excluded Forest Minors and the Erd\H{o}s-P\'osa Property   A classical result of Robertson and Seymour states that the set of graphs
containing a fixed planar graph $H$ as a minor has the so-called
Erd\H{o}s-P\'osa property; namely, there exists a function $f$ depending only
on $H$ such that, for every graph $G$ and every positive integer $k$, the graph
$G$ has $k$ vertex-disjoint subgraphs each containing $H$ as a minor, or there
exists a subset $X$ of vertices of $G$ with $|X| \leq f(k)$ such that $G - X$
has no $H$-minor. While the best function $f$ currently known is exponential in
$k$, a $O(k \log k)$ bound is known in the special case where $H$ is a forest.
This is a consequence of a theorem of Bienstock, Robertson, Seymour, and Thomas
on the pathwidth of graphs with an excluded forest-minor. In this paper we show
that the function $f$ can be taken to be linear when $H$ is a forest. This is
best possible in the sense that no linear bound is possible if $H$ has a cycle.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph