Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decycling Number of Linear Graphs of Trees   The decycling number of a graph $G$ is the minimum number of vertices whose
removal from $G$ results in an acyclic subgraph. It is known that determining
the decycling number of a graph $G$ is equivalent to finding the maximum
induced forests of $G$. The line graphs of trees are the claw-free block
graphs. These graphs have been used by Erd\H{o}s, Saks and S\'{o}s to construct
graphs with a given number of edges and vertices whose maximum induced tree is
very small. In this paper, we give bounds on the decycling number of line
graphs of trees and construct extremal trees to show that these bounds are the
best possible. We also give bounds on the decycling number of line graph of
$k$-ary trees and determine the exact the decycling number of line graphs of
perfect $k$-ary trees.

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The categories of this paper are: cond-mat
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc